[New 2025-26] Chapter 5 - Prime Time NCERT Solution | Worksheet | Extra Questions for Class 6 Maths Ganita Prakash.
Class 6 maths chapter 5 full chapter : Prime time.
Prime Time is a playful adventure through prime numbers, composite numbers, the building blocks of universe of whole numbers, and factorisation...
-
# THIS PAGE INCLUDES :
# Notes : Prime Time.
Prime time class 6 notes.
# Common Multiples and Common Factors :
⇒ Multiple : A number that you get when you multiply a certain number by another number.
E.g.
Multiples of 3 are :
- 3 x 1 = 03
- 3 x 2 = 06
- 3 x 3 = 09
- 3 x 4 = 12
● Properties of Multiples :
- Every multiple of a number is greater than or equal to that number.
- The number of multiples of a given number is infinite.
- Every number is a multiple of itself.
📌 Note : When two different number share same multiple then that same multiple is called the Common Multiple.
⇒ Factor : A factor of a number is an exact divisor of that number.
E.g.
Factors of number 6 :
- 6 ÷ 1 = 6
- 6 ÷ 2 = 3
- 6 ÷ 3 = 2
- 6 ÷ 6 = 1
Here : Number 1, 2, 3 and 6 are exact divisors of 6. So, They are called the factors of 6.
● Properties of Factors :
- 1 is a factor of every number.
- Every number is a factor of itself.
- Every factor of a number is an exact divisor of that number.
- Every factor is less than or equal to the given number.
- Number of factors of a given number are finite.
📌 Note : When two different number share same factor then that same factor is called the Common Factor.
⇒ Perfect Number : A number for which sum of all its factors is equal to twice the number is called a perfect number.
E.g.
Factors of 6 are : 1, 2, 3, 6
Sum of factors = 1 + 2 + 3 + 6 = 12.
Here : The sum of all the factors of number 6 is 12 which is twice of it. Therefore, number 6 is a perfect number.
# Prime Numbers :
⇒ Prime Numbers : The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
E.g. 2, 3, 5, 7, 11, etc.
⇒ Composite Numbers : Numbers having more than two factors other than 1 are called Composite numbers.
E.g. 4, 6, 8, 9, 10, etc.
📌 Note : The number 1 is neither a prime nor a composite number.
# Co-prime Numbers :
When 2 numbers do not have any common factor other than 1 then these 2 numbers are called co-prime numbers.
E.g.
Number 2 and 3 are co-prime numbers as they do not have any common factor other than 1.
Similarly, number 3 and 5, Number 5 and 7, etc. are all co-prime numbers.
📌 Note : Any 2 prime numbers are co-prime numbers.
# Prime Factorisation :
When we break down a number into its individual factors (prime numbers) those factors are called prime factors. The process of braking down a number into its prime factors is known as prime factorisation.
E.g.
Prime Factors of number 28 are : 1, 2 and 7.
# Divisibility Tests :
Divisibility test are used to find out if a number is divisible by another number without long division.
● Rules for Divisibility test of 2, 4, 5, 8 and 10.
- A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.
- A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
- A number which has either 0 or 5 in its ones place is divisible by 5.
- A number with 4 or more digits is divisible by 8, if the number formed by the last 3 digits is divisible by 8.
- If a number has 0 in the ones place then it is divisible by 10.
● Divisibility by 02 :
A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.
E.g. 20, 12, 34, 46, 58, etc.
● Divisibility by 04 :
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
E.g.
- 212 : 12 ÷ 4 = 3
- 288 : 88 ÷ 4 = 22
● Divisibility by 05 :
A number which has either 0 or 5 in its ones place is divisible by 5.
E.g. 25, 40,155, 260, etc.
● Divisibility by 08 :
A number with 4 or more digits is divisible by 8, if the number formed by the last 3 digits is divisible by 8.
E.g.
- 1416 : 416 ÷ 8 = 52
- 2104 : 104 ÷ 8 = 13
● Divisibility by 10 :
If a number has 0 in the ones place then it is divisible by 10.
E.g. 10, 200, 3000, 4120, etc.
----- The End -----
# Key Points :
Class 6 maths chapter 5 explanation :
● If a number is divisible by another, the second number is called a factor of the first. For example, 4 is a factor of 12 because 12 is divisible by 4 (12 ÷ 4 = 3).
● Prime numbers are numbers like 2, 3, 5, 7, 11, … that have only two factors, namely 1 and themselves.
● Composite numbers are numbers like 4, 6, 8, 9, … that have more than 2 factors, i.e., at least one factor other than 1 and themselves. For example, 8 has the factor 4 and 9 has the factor 3, so 8 and 9 are both composite.
● Every number greater than 1 can be written as a product of prime numbers. This is called the number’s prime factorisation. For example, 84 = 2 × 2 × 3 × 7.
● There is only one way to factorise a number into primes, except for the ordering of the factors.
● Two numbers that do not have a common factor other than 1 are said to be co-prime.
● To check if two numbers are co-prime, we can first find their prime factorisations and check if there is a common prime factor. If there is no common prime factor, they are co-prime, and otherwise they are not.
● A number is a factor of another number if the prime factorisation of the first number is included in the prime factorisation of the second number.
# NCERT Solutions :
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 108.
Prime time class 6 ncert solutions.
Q1.
At what number is ‘idli-vada’ said for the 10th time?
Solution :
'Idli-vada' is to be said at the common multiple of 3 and 5. The first common multiple of 3 and 5 is 15.
Here we need to find the 10th common multiple of 3 and 5, which is 150.
Explanation :
1st common multiple of 3 and 5 = 15.
10th common multiple of 3 and 5 = 15 x 10 = 150.
Q2.
If the game is played for the numbers from 1 till 90, find out :
a. How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)?
Solution :
The Children would say 'idli' 30 times between the numbers 1 to 90.
Explanation :
'Idli' is said for multiples of 3. The multiples of 3 between 1 to 90 are : 3, 6, 9, 12, ...., 90. There are (90/3 = 30) 30 multiples of 3.
b. How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)?
Solution :
The Children would say 'vada' 18 times between the numbers 1 to 90.
Explanation :
'vada' is said for multiples of 5. The multiples of 5 between 1 to 90 are : 5, 10, 15, 20, ...., 90. There are (90/5 = 18) 18 multiples of 5.
c. How many times would the children say ‘idli-vada’?
Solution :
The Children would say 'idli-vada' 6 times between the numbers 1 to 90.
Explanation :
'Idli-vada' is said for common multiples of 3 and 5. The common multiples of 3 and 5 between 1 to 90 are : 15, 30, 45, 60, 75 and 90. There are (90/15 = 6) 6 common multiples of 3 and 5.
Q3.
What if the game was played till 900? How would your answers change?
Solution :
If the game was played till 900 then :
● Number of times children said 'idli' :
The Children would say 'idli' 300 times between the numbers 1 to 900.
Explanation :
'Idli' is said for multiples of 3. The multiples of 3 between 1 to 900 are : 3, 6, 9, 12, ...., 900. There are (900/3 = 300) 300 multiples of 3.
● Number of times children said 'vada' :
The Children would say 'vada' 180 times between the numbers 1 to 900.
Explanation :
'vada' is said for multiples of 5. The multiples of 5 between 1 to 900 are : 5, 10, 15, 20, ...., 900. There are (900/5 = 180) 180 multiples of 5.
● Number of times children said 'idli-vada' :
The Children would say 'idli-vada' 60 times between the numbers 1 to 900.
Explanation :
'Idli-vada' is said for common multiples of 3 and 5. The common multiples of 3 and 5 between 1 to 900 are : 15, 30, 45, 60, ...., 900. There are (900/15 = 60) 60 common multiples of 3 and 5.
Q4.
Is this figure somehow related to the ‘idli-vada’ game?
Hint : Imagine playing the game till 30. Draw the figure if the game is played till 60.
Solution :
Yes, it is related to 'idli-vada' game, if we assume multiples of 3 as 'idli' or multiples of 5 and 'vada' and common multiples of 3 and 5 as 'idli-vada'.
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 110.
class 6 maths chapter 5 prime time question answer.
Q1.
Find all multiples of 40 that lie between 310 and 410.
Solution :
The multiples of 40 lie between 310 and 410 are : 320, 360 and 400.
- 40 x 08 =320
- 40 x 09 = 360
- 40 x 10 = 400
Q2.
Who am I?
a. I am a number less than 40. One of my factors is 7. The sum of my digits is 8.
Solution :
7 is the factor of its multiples and multiples of 7 less than 40 are 7, 14, 21, 28, 35.
Here,
The number whose digit sum is 8 = 35 (3 + 5 = 8)
Therefore,
The required number is 35
b. I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other.
Solution :
A number is the factor of its multiple. So 3 and 5 are the factors of its common multiples.
So,
Common multiples of 3 and 5 less than 100 are : 15, 30, 45, 60, 75, 90.
Here,
A number whose one digit is 1 more than other is 45.
Therefore,
The required number is 45.
Q3.
A number for which the sum of all its factors is equal to twice the number is called a perfect number. The number 28 is a perfect number. Its factors are 1, 2, 4, 7, 14 and 28. Their sum is 56 which is twice 28. Find a perfect number between 1 and 10.
Solution :
The perfect number between 1 to 10 is number 6. The factors of number 6 are 1, 2, 3, and 6, and their sum is 12, which is twice of 6.
Q4.
Find the common factors of:
a. 20 and 28.
Solution :
Factors of 20 : 1, 2, 4, 5, 10, 20.
Factors of 28 : 1, 2, 4, 7, 14, 28.
Common Factors of 20 and 28 are : 1, 2 and 4.
b. 35 and 50
Solution :
Factors of 35 : 1, 5, 7, 35.
Factors of 50 : 1, 2, 5, 10, 25, 50.
Common Factors of 35 and 50 are : 1 and 5.
c. 4, 8 and 12
Solution :
Factors of 4 : 1, 2, 4.
Factors of 8 : 1, 2, 4, 8.
Factors of 12 : 1, 2, 4, 6, 12.
Common Factors of 4, 8 and 12 are : 1, 2 and 4.
d. 5, 15 and 25
Solution :
Factors of 05 : 1, 5.
Factors of 15 : 1, 3, 5, 15.
Factors of 25 : 1, 5, 25.
Common Factors of 5, 15 and 25 are : 1 and 5.
Q5.
Find any three numbers that are multiples of 25 but not multiples of 50.
Solution :
Three numbers that are multiple of 25 but not the multiples of 50 are : 75, 125 and 175.
Q6.
Anshu and his friends play the ‘idli-vada’ game with two numbers, which are both smaller than 10. The first time anybody says ‘idli-vada’ is after the number 50. What could the two numbers be which are assigned ‘idli’ and ‘vada’?
Solution :
The two numbers must be 6 and 9.
Explanation :
The two numbers are smaller than 10 and the first time anybody says 'idli-vada' is after the number 50.
So,
The numbers must be the one whose least common multiple is just above 50.
Here,
The numbers 6 and 9 have the least common multiple 54 which is just above 50. This means the first time they say 'idli-vada' is at 54.
Q7.
In the treasure hunting game, Grumpy has kept treasures on 28 and 70. What jump sizes will land on both the numbers?
Solution :
To find the jump sizes, we need to find the common factors of 28 and 70.
Factors of 28 : 1, 2, 4, 7, 14, 28.
Factors of 70 : 1, 2, 5, 7, 10, 14, 35, 70.
Common factors of 28 and 70 are : 1, 2 and 7.
Therefore, jump sizes are 1, 2 and 7.
Q8.
In the diagram below, Guna has erased all the numbers except the common multiples. Find out what those numbers could be and fill in the missing numbers in the empty regions.
Solution :
The numbers in the centre circle are the multiples of 8 and 12. So, the missing numbers in the red circle are the multiples of 8 and in the green circle are the multiples of 12.
Explanation :
Multiple of 8 (red circle) : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
Multiple of 12 (green circle) : 12, 24, 36, 48, 60, 72, 84.
Common multiples of 8 and 12 (centre circle) : 24, 48 and 72.
Q9.
Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.
Solution :
To find the smallest multiple of all the number from 1 to 10 except 7 we need to find their least common multiple (LCM).
The least common multiple of these numbers (2 x 2 x 2 x 3 x 3 x 5) = 360.
Q10.
Find the smallest number that is a multiple of all the numbers from 1 to 10.
Solution :
To find the smallest multiple of all the number from 1 to 10, we need to find their least common multiple (LCM).
The least common multiple of these numbers (2 x 2 x 2 x 3 x 3 x 5 x 7) = 2520.
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 114.
ncert class 6 maths chapter 5 prime time solutions.
Q1.
We see that 2 is a prime and also an even number. Is there any other even prime?
Solution :
No, there is no other even prime number. 2 is the only even prime number.
Q2.
Look at the list of primes till 100. What is the smallest difference between two successive primes? What is the largest difference?
Solution :
The smallest difference between two successive prime numbers up to 100 is (3 - 2) = 1.
The largest difference between two successive prime numbers up to 100 is (97 - 89) = 8.
Explanation :
To find the smallest and largest difference between two successive prime numbers up to 100. we first need to list the prime numbers and find their differences.
List of prime number and their differences up to 100.
| Difference | in | Prime Numbers |
|---|---|---|
| 3 - 2 = 1 | 43 - 41 = 2 | |
| 5 - 3 = 2 | 47 - 43 = 4 | |
| 7 - 5 = 2 | 53 - 47 = 6 | |
| 11 - 7 = 4 | 59 - 53 = 6 | |
| 13 - 11 = 2 | 61 - 59 = 2 | |
| 17 - 13 = 4 | 67 - 61 = 6 | |
| 19 - 17 = 2 | 71 - 67 = 4 | |
| 23 - 19 = 4 | 73 - 71 = 4 | |
| 29 - 23 = 6 | 79 - 73 = 6 | |
| 31 - 29 = 2 | 83 - 79 = 4 | |
| 37 - 31 = 6 | 89 - 83 = 6 | |
| 41 - 37 = 4 | 97 - 89 = 8 |
Q3.
Are there an equal number of primes occurring in every row in the table on the previous page? Which decades have the least number of primes? Which have the most number of primes?
Solution :
There are not equal number of prime numbers in each row. The number of primes varies in every row.
- The decade 91 to 100 have the least number of primes in it that is only 1 prime.
- The decade 1 to 10 and 11 to 19 have the most number of primes in it that is 4 primes.
Q4.
Which of the following numbers are prime? 23, 51, 37, 26
Solution :
Prime numbers are the number that can be divided by only 1 and the number itself.
So, The prime numbers between 23, 51, 37, 26 are 23 and 37.
Q5.
Write three pairs of prime numbers less than 20 whose sum is a multiple of 5.
Solution :
The three pairs of prime numbers less than 20 whose sum is a multiple of 5 are :
- 03 + 7 = 10
- 13 + 2 = 15
- 13 + 7 = 20
Q6.
The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.
Solution :
Pair of prime numbers having same digits are : (1 & 3), (3 & 7) and (1 & 7).
- Numbers have same digits 1 and 3 = 13 and 31
- Numbers have same digits 1 and 7 = 17 and 71
- Numbers have same digits 3 and 7 = 37 and 73
Q7.
Find seven consecutive composite numbers between 1 and 100.
Solution :
Seven consecutive composite numbers between 1 and 100 are : 90, 91, 92, 93, 94, 95 and 96.
Explanation :
A composite number has more than two factors. The numbers from 90 to 96 are all composite and occur consecutively.
Q8.
Twin primes are pairs of primes having a difference of 2. For example, 3 and 5 are twin primes. So are 17 and 19. Find the other twin primes between 1 and 100.
Solution :
Twin primes between 1 to 100 are : (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61) and (71,73).
Q9.
Identify whether each statement is true or false. Explain.
a. There is no prime number whose units digit is 4.
b. A product of primes can also be prime.
c. Prime numbers do not have any factors.
d. All even numbers are composite numbers.
e. 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.
Solution :
a. True (Prime numbers has unit digit 1, 3, 7 and 9)
b. False (Product of prime number 2 and 3 is 6 which is not prime)
c. False (Prime numbers have 2 factors 1 and the number itself)
d. False (Except 2 which is an only even prime number)
e. True (Other than 2 and 3 all prime numbers have a successive composite number)
Q10.
Which of the following numbers is the product of exactly three distinct prime numbers: 45, 60, 91, 105, 330?
Solution :
Number 105 is the product of exactly 3 distinct prime numbers i.e. 3 x 5 x 7 = 105.
Explanation :
- Factors of 45 : 3 x 3 x 5.
- Factors of 60 : 2 x 2 x 3 x 5.
- Factors of 91 : 7 x 13.
- Factors of 105 : 3 x 5 x 7.
- Factors of 330 : 2 x 3 x 5 x 11.
Q11.
How many three-digit prime numbers can you make using each of 2, 4 and 5 once?
Solution :
Numbers formed by using digits 2, 4 and 5 once : 245, 254, 425, 452, 524, 542.
A number is said to be prime only if it has 2 factors that is number 1 or the number itself.
Here,
- Numbers 245 and 425 are divisible by 5, So they have more than 2 factors. Therefore they are not prime.
- Numbers 254, 452, 524 and 542 are divisible by 2, So they have more than 2 factors. Therefore they are not prime.
Q12.
Observe that 3 is a prime number, and 2 × 3 + 1 = 7 is also a prime. Are there other primes for which doubling and adding 1 gives another prime? Find at least five such examples.
Solution :
The five prime numbers for which doubling and adding 1 gives another prime are :
- 02 x 2 + 1 = 05
- 03 x 2 + 1 = 07
- 05 x 2 + 1 = 11
- 11 x 2 + 1 = 23
- 23 x 2 + 1 = 47
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 120.
class 6 maths chapter 5 prime time ncert solutions.
Q1.
Find the prime factorisations of the following numbers: 64, 104, 105, 243, 320, 141, 1728, 729, 1024, 1331, 1000.
Solution :
- Prime Factorisation of 64 : 2 x 2 x 2 x 2 x 2 x 2.
- Prime Factorisation of 104 : 2 x 2 x 2 x 13.
- Prime Factorisation of 105 : 3 x 5 x 7.
- Prime Factorisation of 243 : 3 x 3 x 3 x 3 x 3.
- Prime Factorisation of 320 : 2 x 2 x 2 x 2 x 2 x 2 x 5.
- Prime Factorisation of 141 : 3 x 47.
- Prime Factorisation of 1728 : 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.
- Prime Factorisation of 729 : 3 x 3 x 3 x 3 x 3 x 3.
- Prime Factorisation of 1024 : 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
- Prime Factorisation of 1331 : 11 x 11 x 11.
- Prime Factorisation of 1000 : 2 x 2 x 5 x 5 x 5 x 5.
Q2.
The prime factorisation of a number has one 2, two 3s, and one 11. What is the number?
Solution :
The number is (2 x 3 x 3 x 11) = 198.
Q3.
Find three prime numbers, all less than 30, whose product is 1955.
Solution :
Prime factorization of 1955 = 5 x 17 x 23.
Here, 5, 17 and 23 are prime numbers less than 30.
Q4.
Find the prime factorisation of these numbers without multiplying first
a. 56 × 25
Solution :
Prime factors of 56 : 2 x 2 x 2 x 7.
Prime factors of 25 : 5 x 5.
Combined prime factorisation of 56 and 25 are : 2 x 2 x 2 x 5 x 5 x 7.
b. 108 × 75
Solution :
Prime factors of 108 : 2 x 2 x 3 x 3 x 3.
Prime factors of 75 : 3 x 5 x 5.
Combined prime factorisation of 108 and 75 are : 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5.
c. 1000 × 81.
Solution :
Prime factors of 1000 : 2 x 2 x 2 x 5 x 5 x 5.
Prime factors of 81 : 3 x 3 x 3 x 3.
Combined prime factorisation of 1000 and 81 are : 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 x 5.
Q5.
What is the smallest number whose prime factorisation has:
a. three different prime numbers?
Solution :
The smallest prime numbers are 2, 3 and 5. So the smallest number whose prime factorisation has three different prime numbers is 2 x 3 x 5 = 30.
b. four different prime numbers?
Solution :
The smallest prime numbers are 2, 3, 5 and 7. So the smallest number whose prime factorisation has four different prime numbers is 2 x 3 x 5 x 7 = 210.
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 122.
class 6 maths chapter 5 prime time solutions.
Q1.
Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer.
a. 30 and 45
Solution :
No, 30 and 45 are not co-prime.
Explanation :
The prime factors of 30 are 2 x 3 x 5.
The prime factors of 45 are 3 x 3 x 5.
Here, we see that 3 and 5 are the factors of both 30 and 45. Therefore they are not co-prime.
b. 57 and 85
Solution :
Yes, 57 and 85 are not co-prime.
Explanation :
The prime factors of 57 are 3 x 19.
The prime factors of 85 are 5 x 17.
Here, we see that 30 and 45 have no common factor. Therefore they are co-prime.
c. 121 and 1331
Solution :
No, 121 and 1331 are not co-prime.
Explanation :
The prime factors of 121 are 11 x 11.
The prime factors of 1331 are 11 x 11 x 11.
Here, we see that 11 is the factor of both 121 and 1331. Therefore they are not co-prime.
d. 343 and 216
Solution :
No, 343 and 216 are not co-prime.
Explanation :
The prime factors of 343 are 7 x 7 x 7.
The prime factors of 216 are 2 x 2 x 2 x 3 x 3 x 3.
Here, we see that 30 and 45 have no common factor. Therefore they are co-prime.
Q2.
Is the first number divisible by the second? Use prime factorisation.
a. 225 and 27
Solution :
No, 225 is not divisible by 27.
Explanation :
Prime factorisation of 225 is 3 x 3 x 5 x 5.
Prime factorisation of 27 is 3 x 3 x 3.
Since 27 has three 3s but 225 has only two 3s. So 225 can not be divisible by 27.
b. 96 and 24
Solution :
Yes, 96 is divisible by 24.
Explanation :
Prime factorisation of 24 is 2 x 2 x 2 x 3.
Prime factorisation of 96 is 2 x 2 x 2 x 2 x 2 x 3.
Since 96 has all the factors of 24. So 96 can be divisible by 24.
c. 343 and 17
Solution :
No, 343 is not divisible by 17.
Explanation :
Prime factorisation of 343 is 7 x 7 x 7.
Prime factorisation of 17 is 1 x 17.
Since 343 has no common factor of 17. So 343 can not be divisible by 17.
d. 999 and 99
Solution :
No, 999 is not divisible by 99.
Explanation :
Prime factorisation of 999 is 3 x 3 x 3 x 37.
Prime factorisation of 99 is 3 x 3 x 11.
Since 999 does not have all the factors of 99. So 999 can not be divisible by 99.
Q3.
The first number has prime factorisation 2 × 3 × 7 and the second number has prime factorisation 3 × 7 × 11. Are they co-prime? Does one of them divide the other?
Solution :
- Prime factors of 1st number are 2 x 3 x 7.
- Prime factors of 2nd number are 3 x 7 x 11.
The given two numbers are not co-prime as they have common factors 3 and 7.
Here, The first number is missing the prime factor 11 and the second number is missing the prime factor 2. So they both can not divide each other.
Q4.
Guna says, “Any two prime numbers are co-prime”. Is he right?
Solution :
Yes, Guna is right because any two prime numbers have no common factor other than 1.
Ganita Prakash class 6 maths chapter 5 prime time figure it out page 125.
ncert solutions for class 6 maths chapter 5 prime time.
Q1.
2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, except for those years that are evenly divisible by 100 but not 400.
a. From the year you were born till now, which years were leap years?
Solution :
From the year 2012 to 2024 there are 4 leap years. 2012, 2016, 2020 and 2024.
b. From the year 2024 till 2099, how many leap years are there?
Solution :
From the year 2024 to 2099 there will be 19 leap years.
[ 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080, 2084, 2088, 2092, and 2096 ]
Q2.
Find the largest and smallest 4-digit numbers that are divisible by 4 and are also palindromes.
Solution :
- Largest 4 digit number that is divisible by 4 and also palindrome is 8888.
- Smallest 4 digit number that is divisible by 4 and also palindrome is 2112.
Q3.
Explore and find out if each statement is always true, sometimes true or never true. You can give examples to support your reasoning.
a. Sum of two even numbers gives a multiple of 4.
Solution :
Sometimes true.
Explanation :
Some of any two even numbers is not always divisible by 4.
E.g.
6 + 4 = 10
2 + 4 = 06
Here, 10 and 6 are not divisible by 4.
b. Sum of two odd numbers gives a multiple of 4.
Solution :
Sometimes true.
Explanation :
Some of any two odd numbers is not always divisible by 4.
E.g.
03 + 07 = 10
11 + 03 = 14
Here, 10 and 14 are not divisible by 4.
Q4.
Find the remainders obtained when each of the following numbers are divided by -
i) 10,
ii) 5,
iii) 2.
78, 99, 173, 572, 980, 1111, 2345
Solution :
Number 78 :
- Divisible by 10 : 78 ÷ 10 = 08 (remainder = 8)
- Divisible by 05 : 78 ÷ 05 = 15 (remainder = 3)
- Divisible by 02 : 78 ÷ 02 = 39 (remainder = 0)
Number 99 :
- Divisible by 10 : 99 ÷ 10 = 09 (remainder = 9)
- Divisible by 05 : 99 ÷ 05 = 19 (remainder = 4)
- Divisible by 02 : 99 ÷ 02 = 49 (remainder = 1)
Number 173 :
- Divisible by 10 : 173 ÷ 10 = 17 (remainder = 3)
- Divisible by 05 : 173 ÷ 05 = 34 (remainder = 3)
- Divisible by 02 : 173 ÷ 02 = 86 (remainder = 1)
Number 572 :
- Divisible by 10 : 572 ÷ 10 = 057 (remainder = 2)
- Divisible by 05 : 572 ÷ 05 = 114 (remainder = 2)
- Divisible by 02 : 572 ÷ 02 = 286 (remainder = 0)
Number 980 :
- Divisible by 10 : 980 ÷ 10 = 098 (remainder = 0)
- Divisible by 05 : 980 ÷ 05 = 196 (remainder = 0)
- Divisible by 02 : 980 ÷ 02 = 490 (remainder = 0)
Number 1111 :
- Divisible by 10 : 1111 ÷ 10 = 111 (remainder = 1)
- Divisible by 05 : 1111 ÷ 05 = 222 (remainder = 1)
- Divisible by 02 : 1111 ÷ 02 = 555 (remainder = 1)
Number 2345 :
- Divisible by 10 : 2345 ÷ 10 = 0234 (remainder = 5)
- Divisible by 05 : 2345 ÷ 05 = 0469 (remainder = 0)
- Divisible by 02 : 2345 ÷ 02 = 1172 (remainder = 1)
Q5.
The teacher asked if 14560 is divisible by all of 2, 4, 5, 8 and 10. Guna checked for divisibility of 14560 by only two of these numbers and then declared that it was also divisible by all of them. What could those two numbers be?
Solution :
The two key numbers to check divisibility would be 8 and 10. because if a number is divisible by 8 and 10 then it will be divisible by 2, 4 and 5 as well.
Q6.
Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10 : 572, 2352, 5600, 6000, 77622160.
Solution :
The number which is divisible by 2, 4, 5, 8 and 10 are : 5600, 6000, 77622160.
Explanation :
The two key numbers to check divisibility would be 8 and 10. because if a number is divisible by 8 and 10 then it will be divisible by 2, 4 and 5 as well.
Q7.
Write two numbers whose product is 10000. The two numbers should not have 0 as the units digit.
Solution :
The two number whose product is 10000 and does not have '0' as the unit digit are : 16 and 625.
Explanation :
Prime factorisation of 10000 : (2 x 2 x 2 x 2) x (5 x 5 x 5 x 5).
Prime factorisation of 10000 : (16 x 625)
# Worksheet - Extra Questions :
Class 6 maths chapter 5 prime time extra questions.
Prime time class 6 worksheet cbse.
# Fill in the blanks :
1. Numbers having more than two factors are called __________ numbers.
2. _____ is a factor of every number.
3. A number is a _____ of each of its factor.
4. The number of factors of a prime number is_____.
5. Two numbers having only 1 as a common factor are called_____ numbers.
# True - False :
1. Every multiple of a number is greater than or equal to the number.
2. The number of multiples of a given number is finite.
3. Every number is a multiple of itself.
4. Sum of two consecutive odd numbers is always divisible by 4.
5. If a number is divisible both by 2 and 3, then it is divisible by 12.
Prime time class 6 mcq questions.
# Multiple Choice Questions :
Q1. The sum of first three common multiples of 3, 4 and 9 is ?
(a) 108
(b) 144
(c) 252
(d) 216
Q2. Sum of the number of primes between 16 to 80 and 90 to 100 is ?
(a) 20
(b) 18
(c) 17
(d) 16
Q3. The number of distinct prime factors of the smallest 5-digit number is ?
(a) 2
(b) 4
(c) 6
(d) 8
Q4. A number is divisible by 5 and 6. It may not be divisible by ?
(a) 10
(b) 15
(c) 30
(d) 60
Q5. The sum of the prime factors of 1729 is ?
(a) 13
(b) 19
(c) 32
(d) 39
Class 6 maths chapter 5 prime time exercise.
# Numerical Question :
Q1.
Determine the least number which when divided by 3, 4 and 5 leaves remainder 2 in each case.
Q2.
Find a 4-digit odd number using each of the digits 1, 2, 4 and 5 only once such that when the first and the last digits are interchanged, it is divisible by 4.
Q3.
In a colony of 100 blocks of flats numbering 1 to 100, a school van stops at every sixth block while a school bus stops at every tenth block. On which stops will both of them stop if they start from the entrance of the colony?
Q4.
Using each of the digits 1, 2, 3 and 4 only once, determine the smallest 4-digit number divisible by 4.
Q5.
Using divisibility test. determine which of the following numbers are divisible by 4?
(a) 4096
(b) 21084
Prime time class 6 extra questions worksheet with answer.
Class 6 maths chapter 5 prime time worksheet.
# Fill in the Blanks :
1. Composite
2. 1
3. Multiple
4. 2
5. Co-prime
# True - False :
1. True
2. False
3. True
4. True
5. False
Prime time class 6 extra questions mcq
# MCQ's :
1. 216 (d)
2. 17 (c)
3. 2 (a)
4. 60 (d)
5. 39 (d)
Prime time class 6 extra questions.
# Numerical Questions :
Solution Q1 :
To find the least number which is divisible by 3, 4 and 5 with remainder 2. we need to find the least common multiple of 3, 4 and 5 and then add 2 to the number obtained.
Least common multiple of 3, 4 and 5 (3 x 4 x 5) = 60
Now, add the remainder 2 to the least common multiple = 60 + 2 = 62.
Therefore, the required number is 62.
Solution Q2 :
The possible 4 digit odd numbers using digits 1, 2, 4 and 5 are :
[ 4215, 4125, 1245, 1425, 2145, 2415, 4521, 4251, 2541, 2451, 5241 and 5421 ]
When first and last digit interchanged, the new 4 digit numbers are :
[ 5214, 5124, 5241, 5421, 5142, 5412, 1524, 1254, 1542, 1452, 1245 and 1425 ]
Now, the numbers which are divisible by 4 are : 5124, 5412, 1524, 1452.
Therefore,
The required 4-digit odd numbers which is divisible by 4 is (any one) : 4125, 2415, 4521, 2451.
Solution Q3 :
Number of blocks in the colony = 100
School van stops at every block = 6
School bus stops at every block = 10
The blocks at which they both stop = Common multiples of 6 and 10
Now,
Multiple of 6 from 1 to 100 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96.
Multiple of 10 from 1 to 100 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
Common multiples of 6 and 10 = 30, 60, 90.
Therefore,
The blocks at which both van and bus will stop are Block 30, 60, 90.
Solution Q4 :
The possible 4 digit numbers made using digits 1, 2, 3 and 4 are :
[1234, 1324, 1432, 1243, 1342, 1423, 2134, 2341, 2431, 2143, 2314, 2413, 3124, 3241, 3421, 3142, 3214, 3412, 4123, 4231, 4321, 4132, 4213, 4312]
Now, the numbers which are divisible by 4 are : 1324, 1432, 3124, 3412, 4132, 4312.
Therefore,
The required smallest 4-digit numbers which is divisible by 4 is : 1324.
Solution Q5 :
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
(a) 4096
Last two Digits of number 4096 are 96 which are divisible by 4 (96 ÷ 4 = 24). Therefore, the number 4096 is also divisible by 4.
(b) 21084
Last two Digits of number 21084 are 84 which are divisible by 4 (84 ÷ 4 = 21). Therefore, the number 21084 is also divisible by 4.
# MCQ Test :
# Still have some Doubts?
--Feel FREE to Ask you Doubts Here--
# Learn More :
CBSE Class 6th Mathematics teaches students about the basics, which have a wide range of application in their higher studies. All the chapters given below includes Solutions for all the question available in Class 6th Mathematics NCERT Textbook Ganita Prakash. It also includes some Important Extra Questions related to the Chapters and we have also provided Free Quiz Based Test which is consist of Objective Type Questions which help the students to test their Understanding about the given Chapters. This material is available for Free For the Students So that they can prepare & score good marks in their upcoming exams.
| Chapters | Class 6 Maths Syllabus |
|---|---|
| Chapter 01 : | Patterns in Mathematics |
| Chapter 02 : | Lines and Angles |
| Chapter 03 : | Number Play |
| Chapter 04 : | Data Handling and Presentation |
| Chapter 05 : | Prime Time |
| Chapter 06 : | Perimeter and Area |
| Chapter 07 : | Fractions |
| Chapter 08 : | Playing with Constructions |
| Chapter 09 : | Symmetry |
| Chapter 10 : | The Other Side of Zero |
Curiosity, Textbook of Science for Grade 6, comprises twelve chapters. As the name of the textbook suggests, there are numerous opportunities for the learners to explore the world of science and its nature. Through the chapters, learners will embark on a journey that will connect them to the world around and spark curiosity for further exploration. The hands-on activities embedded within each chapter engages the learners and provide them an opportunity to reflect on learning. The primary aim of Curiosity is to prepare the children for becoming the responsible members of the society, and therefore efforts have been made to raise awareness about various issues, such as gender, region, environment, health and hygiene, water scarcity and energy conservation.
| Chapters | Class 6 Science Syllabus |
|---|---|
| Chapter 01 : | The Wonderful World of Science |
| Chapter 02 : | Diversity in the Living World |
| Chapter 03 : | Mindful Eating: A Path to a Healthy Body |
| Chapter 04 : | Exploring Magnets |
| Chapter 05 : | Measurement of Length and Motion |
| Chapter 06 : | Materials Around Us |
| Chapter 07 : | Temperature and its Measurement |
| Chapter 08 : | A Journey through States of Water |
| Chapter 09 : | Methods of Separation in Everyday Life |
| Chapter 10 : | Living Creatures: Exploring their Characteristics |
| Chapter 11 : | Nature’s Treasures |
| Chapter 12 : | Beyond Earth |
Class 6th English NCERT Poorvi has five thematic units that comprise stories, poems, conversation, narrative and descriptive pieces. Themes such as friendship, wellness, sports, nature, art and culture, etc. have been included. Cross-cutting themes, such as Indian Knowledge Systems, values, heritage, gender sensitivity and inclusion have been integrated in all the units. Each unit has three literary pieces― story or conversation, poem and non-fiction. There are intext questions, ‘Let us discuss’ to assess comprehension of the text. The end-of-the-text questions given in ‘Let us think and reflect’ are designed to encourage critical thinking, reasoning, responding, analyzing, etc. These literary pieces are not only entertaining but also instill valuable life lessons, fostering personal growth and helping children navigate social situations with confidence. The selected pieces will resonate with children’s daily experiences and encourage positive values like resilience, empathy and emotional intelligence that can have a profound impact on their development.
| No. | Class 6 English Syllabus |
|---|---|
| Unit 1 : | Fables and Folk Tales |
| A Bottle of Dew | |
| The Raven and The Fox | |
| Rama to the Rescue | |
| Unit 2 : | Friendship |
| The Unlikely Best Friends | |
| A Friend's Prayer | |
| The Chair | |
| Unit 3 : | Nurturing Nature |
| Neem Baba | |
| What a Bird Thought | |
| Spices that Heal Us | |
| Unit 4 : | Sports and Wellness |
| Change of Heart | |
| The Winner | |
| Yoga - A Way of Life | |
| Unit 5 : | Culture and Tradition |
| Hamara Bharat - Incredible India! | |
| The Kites | |
| Ila Sachani : Embroidering Dreams with her Feet | |
| National War Memorial |
