Factors and Multiples - Worksheet Digital - Free Printable

Let's solve each part of the worksheet step by step.

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Understanding Factors

Factors are numbers that divide exactly into another number (with no remainder).
For example:
- The factors of 12: 1, 2, 3, 4, 6, 12 → because these numbers divide 12 evenly.
- They can be paired as:
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12

We'll use this method to find the factors of each number.

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a) List the factors of 9

We look for all whole numbers that divide 9 exactly.

Try dividing 9 by numbers starting from 1:

- 1 × 9 = 9 → both 1 and 9 are factors
- 2 × ? = 9 → not a whole number (9 ÷ 2 = 4.5) → not a factor
- 3 × 3 = 9 → so 3 is a factor
- 4, 5, 6, 7, 8 → don’t divide 9 evenly
- 9 × 1 = 9 → already counted

So the factors of 9 are:
1, 3, 9

✔ Answer: 1, 3, 9

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b) List the factors of 16

Check which numbers divide 16 evenly:

- 1 × 16 = 16 → 1 and 16 are factors
- 2 × 8 = 16 → 2 and 8 are factors
- 4 × 4 = 16 → 4 is a factor
- 5? 16 ÷ 5 = 3.2 → no
- 6? 16 ÷ 6 ≈ 2.67 → no
- 7? 16 ÷ 7 ≈ 2.29 → no
- 8? already have it
- Stop at √16 = 4, so we’ve covered all

So the factors are:
1, 2, 4, 8, 16

✔ Answer: 1, 2, 4, 8, 16

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c) List the factors of 25

Check divisors of 25:

- 1 × 25 = 25 → 1 and 25
- 5 × 5 = 25 → 5 is a factor
- 2? 25 ÷ 2 = 12.5 → no
- 3? 25 ÷ 3 ≈ 8.33 → no
- 4? 25 ÷ 4 = 6.25 → no
- 6–24? none divide evenly

So the factors are:
1, 5, 25

✔ Answer: 1, 5, 25

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d) List the factors of 24

Now check numbers that divide 24:

- 1 × 24 = 24 → 1, 24
- 2 × 12 = 24 → 2, 12
- 3 × 8 = 24 → 3, 8
- 4 × 6 = 24 → 4, 6
- 5? 24 ÷ 5 = 4.8 → no
- 6? already have
- 7? 24 ÷ 7 ≈ 3.43 → no
- 8? already have
- Continue up to √24 ≈ 4.9 → so we've checked enough

List all unique factors:
1, 2, 3, 4, 6, 8, 12, 24

✔ Answer: 1, 2, 3, 4, 6, 8, 12, 24

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✔ Final Answers:

a) 1, 3, 9
b) 1, 2, 4, 8, 16
c) 1, 5, 25
d) 1, 2, 3, 4, 6, 8, 12, 24

Let me know if you'd like these listed in pairs or explained further!