Class 6 Chapter 5 Prime Time Worksheet for NCERT Book

Here is a worksheet for class 6 students for chapter 5, Prime time. We suggest the students to solve the questions after completing the chapter. The questions are a bit challenging.

Class 6 Mathematics – Prime Time (NCERT) | Practice Set: Challenging

A. Multiples & Factors (Idli–Vada Style)

1. In the ‘idli-vada’ game, ‘idli’ is said for multiples of 4 and ‘vada’ for multiples of 6.
   • (a) What is the first number for which ‘idli-vada’ will be said?
   • (b) How many times will ‘idli-vada’ be said between 1 and 120?
2. The first time ‘idli-vada’ is said after 60 when playing with two numbers smaller than 10.
   What could those two numbers be? Write any one possible pair with a reason.
3. Find all multiples of 36 that lie between 200 and 350.
4. Two numbers have 12 as their first common multiple. One of the numbers is 3.
   Find all possible values of the other number.
5. In the Jump Jackpot game, treasures are placed on 18 and 42.
   Find all the jump sizes that will land on both numbers.

B. Prime & Composite Numbers

6. Write all the numbers between 40 and 60 and classify them as:
   • Prime
   • Composite
   • Neither prime nor composite
7. How many prime numbers are there between 50 and 100?
   Name the smallest and the largest prime in this range.
8. Find three pairs of prime numbers less than 30 whose sum is a multiple of 6.
9. Which of the following are prime?
   91, 97, 121, 131
   Give a reason for each answer.
10. Find:
    • (a) Five consecutive composite numbers
    • (b) Two pairs of twin primes between 1 and 50

C. Co-Prime Numbers

11. Check whether the following pairs are co-prime:
    • (a) 24 and 35
    • (b) 49 and 64
    • (c) 27 and 40
12. Two numbers are both less than 15 and are co-prime.
    Their product is 84. What could the two numbers be?
13. Give one example each where:
    • (a) First common multiple = product of the numbers
    • (b) First common multiple < product of the numbers
14. Out of the pairs below, identify the safe pairs for the treasure game:
    • 14 and 25
    • 16 and 27
    • 18 and 24
    • 35 and 48

D. Prime Factorisation & Divisibility

15. Find the prime factorisation of:
    • (a) 360
    • (b) 504
16. A number has prime factorisation 2 × 2 × 3 × 5 × 7.
    Find the number and state whether it is divisible by 60.
17. Without multiplying first, find the prime factorisation of:
    • (a) 48 × 25
    • (b) 81 × 40
18. Using prime factorisation, check whether:
    • (a) 540 is divisible by 18
    • (b) 770 is divisible by 28
19. Find the smallest number that is divisible by all the numbers from 1 to 8.
20. A 4-digit number is divisible by 2, 4, 5, and 8.
    What must be the last three digits of the number? Explain in one or two lines.

Class 6 Mathematics – Answer Key

Chapter 5: Prime Time (NCERT) | Answers with brief reasoning

A. Multiples & Factors

1. LCM of 4 and 6 = 12.
   • (a) First ‘idli-vada’ = 12
   • (b) Between 1 and 120: 120 ÷ 12 = 10 times
2. One possible pair: 7 and 9.
   LCM = 63, which is the first ‘idli-vada’ after 60.
3. Multiples of 36 between 200 and 350 are 216, 252, 288, 324.
4. LCM is 12 and one number is 3.
   The other number can be 4, 6, or 12.
5. Factors of 18: 1, 2, 3, 6, 9, 18
   Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
   Common jump sizes are 1, 2, 3, 6.

B. Prime & Composite Numbers

6. Primes: 41, 43, 47, 53, 59.
   Composite: all other numbers from 40 to 60.
   Neither prime nor composite: None.
7. There are 10 primes between 50 and 100.
   Smallest = 53, largest = 97.
8. Examples:
   • 5 + 7 = 12 (multiple of 6)
   • 11 + 13 = 24 (multiple of 6)
   • 17 + 19 = 36 (multiple of 6)
9. • 91 = 7 × 13, so it is composite.
   • 97 is not divisible by 2, 3, 5, or 7, so it is prime.
   • 121 = 11 × 11, so it is composite.
   • 131 is not divisible by 2, 3, 5, 7, 11, or 13, so it is prime.
10. • (a) 24, 25, 26, 27, 28
    • (b) Twin primes: (11, 13) and (17, 19)

C. Co-Prime Numbers

11. • (a) 24 and 35 are co-prime (no common factor other than 1).
    • (b) 49 and 64 are co-prime (49 = 7², 64 = 2⁶).
    • (c) 27 and 40 are co-prime (27 = 3³, 40 = 2³ × 5).
12. One possible pair is 12 and 7 since 12 × 7 = 84 and they are co-prime.
13. • (a) 4 and 9 are co-prime, so LCM = 4 × 9 = 36.
    • (b) 6 and 9 are not co-prime, so LCM = 18, which is less than 54.
14. Safe pairs (co-prime) are 14 and 25, and 16 and 27.
    The other pairs share a common factor greater than 1.

D. Prime Factorisation & Divisibility

15. • 360 = 2 × 2 × 2 × 3 × 3 × 5
    • 504 = 2 × 2 × 2 × 3 × 3 × 7
16. 2 × 2 × 3 × 5 × 7 = 420.
    Since 60 = 2 × 2 × 3 × 5, 420 contains all these factors, so it is divisible by 60.
17. • 48 × 25 = (2⁴ × 3) × (5²) = 2⁴ × 3 × 5²
    • 81 × 40 = (3⁴) × (2³ × 5) = 2³ × 3⁴ × 5
18. • (a) 540 = 2² × 3³ × 5 and 18 = 2 × 3², so 540 is divisible by 18.
    • (b) 770 = 2 × 5 × 7 × 11 and 28 = 2² × 7, so 770 is not divisible by 28.
19. The smallest number divisible by 1 to 8 is LCM(1,2,3,4,5,6,7,8) = 840.
20. It must end in 0 (divisible by 5) and the last three digits must be divisible by 8.
    So the last three digits can be 120, 240, 360, 480, 600, 720, 840, 960.

Other Worksheets for Class 6

• Chapter 3 Number Play Worksheet
• Chapter 6 Perimeter and Area Worksheet
• Chapter 7 Fractions Worksheet
• Chapter 10 The Other Side of Zero Worksheet