Prime Time — Mastery

Q1. How many times would the children say 'vada' (including the times they say 'idli-vada') in the idli-vada game played from 1 to 90?

• A. 18
• B. 12
• C. 9
• D. 30

Q2. How many factors does 36 have of Ganita Prakash?

• A. 9
• B. 6
• C. 8
• D. 12

Q3. Find the common factors of 35 and 50.

• A. 1 and 5
• B. 1, 5 and 7
• C. 5 and 7
• D. 1, 5, 7 and 10

Q4. Find the common factors of 4, 8 and 12.

• A. 1, 2 and 4
• B. 2 and 4
• C. 1 and 2
• D. 1, 2, 3 and 4

Q5. Anshu wants to arrange 7 figs in a rectangular array. Why is only one arrangement (1 × 7) possible?

• A. Because 7 is a prime number with only two factors — 1 and 7
• B. Because 7 is an odd number
• C. Because 7 is a composite number
• D. Because 7 is a multiple of itself

Q6. Guna can arrange 12 figs in a rectangular shape in more than one way. What does this tell us about 12?

• A. 12 is a prime number
• B. 12 is a perfect number
• C. 12 is a square number
• D. 12 is a composite number with more than two factors

Q7. Find seven consecutive composite numbers between 1 and 100.

• A. 90, 91, 92, 93, 94, 95, 96
• B. 30, 31, 32, 33, 34, 35, 36
• C. 50, 51, 52, 53, 54, 55, 56
• D. 21, 22, 23, 24, 25, 26, 27

Q8. Looking at the list of primes till 100, what is the smallest difference between two successive primes?

• A. 1
• B. 0
• C. 2
• D. 3

Q9. What is the largest gap between two successive primes in the list of primes till 100?

• A. 4
• B. 6
• C. 10
• D. 8

Q10. Observe that 3 is a prime and 2 × 3 + 1 = 7 is also a prime. For which of the following primes p is 2p + 1 also a prime?

• A. p = 7
• B. p = 13
• C. p = 17
• D. p = 11

Q11. How many three-digit prime numbers can you make using each of the digits 2, 4 and 5 exactly once?

• A. 6
• B. 3
• C. 1
• D. 0

Q12. Which of the following is a pair of primes less than 20 whose sum is a multiple of 5?

• A. 3 and 7
• B. 5 and 7
• C. 11 and 13
• D. 7 and 11

Q13. Are 18 and 35 a co-prime pair?

• A. Yes — their only common factor is 1
• B. No — they share the factor 3
• C. No — they share the factor 5
• D. Cannot tell without prime factorisation

Q14. Anshu notices that when she plays 'idli-vada' with the pair (3, 5), the first common multiple is 15 — which equals 3 × 5. When does the first common multiple of two numbers equal their product?

• A. Always
• B. Only when one of them is prime
• C. Whenever the two numbers are both even
• D. Whenever the two numbers are co-prime

Q15. What is the prime factorisation of 64?

• A. 2 × 2 × 2 × 2 × 2 × 2
• B. 2 × 2 × 16
• C. 4 × 4 × 4
• D. 8 × 8

Q16. What is the prime factorisation of 104?

• A. 2 × 4 × 13
• B. 8 × 13
• C. 4 × 26
• D. 2 × 2 × 2 × 13

Q17. What is the prime factorisation of 243?

• A. 3 × 81
• B. 9 × 27
• C. 3 × 3 × 3 × 3 × 3
• D. 3 × 9 × 9

Q18. The prime factorisation of a number has one 2, two 3s and one 11. What is the number?

• A. 66
• B. 132
• C. 99
• D. 198

Q19. Find the prime factorisation of 56 × 25 without multiplying first.

• A. 2 × 2 × 2 × 7 × 5 × 5
• B. 2 × 2 × 7 × 5 × 5
• C. 2 × 2 × 2 × 7 × 25
• D. 8 × 7 × 25

Q20. What is the smallest number whose prime factorisation has three different prime numbers?

• A. 15
• B. 42
• C. 60
• D. 30

Q21. Using prime factorisation, is 96 divisible by 24?

• A. No, because 96 has more prime factors than 24
• B. No, because 96 is even and 24 is even
• C. Yes, because both are multiples of 12
• D. Yes, because 24 = 2 × 2 × 2 × 3 appears within 96 = 2 × 2 × 2 × 2 × 2 × 3

Q22. Is 8536 divisible by 4?

• A. No, because 8536 ends in 6
• B. No, because 8536 is not divisible by 8
• C. Yes, because 8536 is even
• D. Yes, because 36 (last two digits) is divisible by 4

Q23. The rule for divisibility by 8 is: a number is divisible by 8 if and only if

• A. Its last digit is 8
• B. Its last two digits form a multiple of 8
• C. It is divisible by 2 and 4
• D. The number formed by its last three digits is divisible by 8

Q24. Find a perfect number between 1 and 10. (Recall: a perfect number equals twice the sum of its own factors equals 2× the number — i.e., the sum of all factors of the number, including itself, equals twice the number.)

• A. 4
• B. 8
• C. 6
• D. 9

Q25. '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.' Who am I?

• A. 15
• B. 75
• C. 30
• D. 45

Q26. A Class 6 student tells the teacher, '1 is a prime number because it has no other factor.' Which is the BEST way for the teacher to address this misconception?

• A. Tell the student '1 is not prime' and move on
• B. Mark the answer wrong in the notebook
• C. Tell the student that 1 is the smallest composite number
• D. Ask the student to list the factors of 1, count them, and compare with the definition that a prime has exactly two factors

Q27. Priya tells her teacher, 'All odd numbers are prime.' Which is the most effective example for the teacher to use to disprove this?

• A. Show that 7 is odd and prime
• B. Show that 9 is odd but 9 = 3 × 3, so 9 is composite
• C. Show that 2 is the only even prime
• D. Tell Priya the statement is wrong

Q28. A teacher wants Class 6 students to discover that prime factorisation is unique. Which classroom strategy is most aligned with the chapter's approach ?

• A. Give the formula and ask students to memorise it
• B. Test only the multiplication: 2 × 2 × 3 × 3 = 36
• C. Show one tree on the board and say 'this is the answer'
• D. Ask different students to build factor trees for 36 starting differently (2×18, 4×9, 6×6) and compare the final primes

Q29. A number is divisible by 5 if its last digit is

• A. 0 only
• B. 5 only
• C. Any even digit
• D. 0 or 5

Q30. What is the smallest number whose prime factorisation has four different prime numbers?

• A. 120
• B. 60
• C. 210
• D. 420