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# Factors and Multiples
*(Choose the correct answer from the options given below)*
Q1. Which of the following is a factor of 24?
- a) 5
- b) 7
- c) 6
- d) 9
Q2. What is the smallest multiple of 8?
- a) 1
- b) 0
- c) 16
- d) 8
Q3. How many factors does the number 12 have?
- a) 4
- b) 5
- c) 6
- d) 3
Q4. Which number is a common factor of both 18 and 24?
- a) 5
- b) 7
- c) 6
- d) 8
Q5. Which of the following is the 5th multiple of 7?
- a) 21
- b) 28
- c) 42
- d) 35
*(Fill in the blanks with the correct answer)*
Q6. The factors of 10 are 1, 2, 5, and ________.
Q7. The first three multiples of 9 are 9, 18, and ________.
Q8. A number that has only two factors — 1 and itself — is called a ________ number.
Q9. The common multiples of 2 and 3 that come before 20 are 6, 12, and ________.
Q10. Every number is both a factor and a multiple of ________.
*(Answer the following questions in 2–3 lines)*
Q11. Write all the factors of 36.
Q12. Find the first five multiples of 11.
Q13. Is 5 a factor of 65? Show your working to explain your answer.
Q14. What is the difference between a factor and a multiple? Give one example of each.
Q15. Find the common factors of 16 and 24.
| Question | Answer | Explanation |
|----------|--------|-------------|
| Q1 | c) 6 | 24 ÷ 6 = 4, so 6 divides 24 exactly |
| Q2 | d) 8 | The smallest non-zero multiple of any number is the number itself |
| Q3 | c) 6 | Factors of 12: 1, 2, 3, 4, 6, 12 → 6 factors |
| Q4 | c) 6 | 18 ÷ 6 = 3 ✓ and 24 ÷ 6 = 4 ✓ |
| Q5 | d) 35 | 7 × 5 = 35 |
| Question | Answer | Explanation |
|----------|--------|-------------|
| Q6 | 10 | 10 ÷ 10 = 1, so 10 is a factor of itself |
| Q7 | 27 | 9 × 3 = 27 |
| Q8 | Prime | E.g., 2, 3, 5, 7 have only two factors |
| Q9 | 18 | 18 is divisible by both 2 and 3 |
| Q10 | Itself | E.g., 5 × 1 = 5, and 5 ÷ 5 = 1 |
Q11. Factors of 36:
> 1, 2, 3, 4, 6, 9, 12, 18, 36
*(Total: 9 factors)*
Q12. First five multiples of 11:
> 11 × 1 = 11
> 11 × 2 = 22
> 11 × 3 = 33
> 11 × 4 = 44
> 11 × 5 = 55
Q13. Is 5 a factor of 65?
> 65 ÷ 5 = 13 (no remainder)
> Since 65 divides exactly by 5, Yes, 5 is a factor of 65.
Q14. Difference between Factor and Multiple:
> - A factor is a number that divides another number exactly.
> *Example: 4 is a factor of 20 (20 ÷ 4 = 5)*
> - A multiple is a number obtained by multiplying a number by 1, 2, 3, …
> *Example: 20 is a multiple of 4 (4 × 5 = 20)*
Q15. Common factors of 16 and 24:
> Factors of 16 → 1, 2, 4, 8, 16
> Factors of 24 → 1, 2, 3, 4, 6, 8, 12, 24
> Common Factors = 1, 2, 4, 8
*🌟 Well done! Keep practising!*
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