1. Which of the following is a multiple of 7?
- A27
- B35
- C44
- D48
Show answer
Answer: B) 35
35 ÷ 7 = 5 exactly, so 35 is a multiple of 7. The others leave a remainder when divided by 7.
Class 6 Playing with Numbers — practice questions with answers
Playing with Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Which of the following is the correct prime factorisation of 36?
- A2 × 2 × 3 × 3
- B2 × 3 × 6
- C4 × 9
- D2 × 2 × 9
Show answer
Answer: A) 2 × 2 × 3 × 3
36 = 4 × 9 = (2 × 2) × (3 × 3). So the prime factorisation is 2 × 2 × 3 × 3.
3. A number is divisible by 6. Which statement must be true?
- AIt is divisible by both 2 and 3.
- BIt is divisible by 4.
- CIt is divisible by 9.
- DIt is an odd number.
Show answer
Answer: A) It is divisible by both 2 and 3.
Since 6 = 2 × 3, any number divisible by 6 is divisible by both 2 and 3. It need not be divisible by 4 or 9, and it is even (not odd).
4. Which number below is a common multiple of 6 and 8 but is NOT the LCM of 6 and 8?
- A12
- B24
- C36
- D48
Show answer
Answer: D) 48
The common multiples of 6 and 8 are 24, 48, 72, … . The smallest is 24, so 24 is the LCM; 48 comes next (48 ÷ 6 = 8 and 48 ÷ 8 = 6), which makes it common but not least. The traps 12 and 36 are multiples of 6 only — neither one divides evenly by 8.
5. Test the rule 'HCF × LCM = product of the two numbers' on 15 and 20. Which line below is correct?
- AHCF 10 × LCM 30 = 300, which matches 15 × 20.
- BHCF 5 × LCM 60 = 300, which matches 15 × 20.
- CHCF 5 × LCM 60 = 300, but 15 × 20 = 350, so the rule fails.
- DThe rule holds only when the two numbers are co-prime.
Show answer
Answer: B) HCF 5 × LCM 60 = 300, which matches 15 × 20.
Factors of 15: 1, 3, 5, 15; factors of 20: 1, 2, 4, 5, 10, 20 — so the HCF is 5. Multiples of 15: 15, 30, 45, 60; multiples of 20: 20, 40, 60 — so the LCM is 60. Then 5 × 60 = 300 and 15 × 20 = 300. The traps: 10 is not a factor of 15 at all, 15 × 20 is 300 and not 350, and the rule works for every pair of numbers, not only co-primes.
Practise all 90 questions free →
10 free questions a day without an account — unlimited with a free account.