Factors and Multiples Worksheets - Math Monks - Free Printable

Sure! Let’s solve each problem step by step and explain the reasoning.

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1) Write the first 2 multiples of:

A multiple of a number is the product of that number and any whole number (starting from 1).

- a) 5
→ 5 × 1 = 5
→ 5 × 2 = 10
✔ First 2 multiples: 5, 10

- b) 12
→ 12 × 1 = 12
→ 12 × 2 = 24
✔ First 2 multiples: 12, 24

- c) 4
→ 4 × 1 = 4
→ 4 × 2 = 8
✔ First 2 multiples: 4, 8

- d) 18
→ 18 × 1 = 18
→ 18 × 2 = 36
✔ First 2 multiples: 18, 36

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2) Circle the numbers that are multiples of 7.

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ...

Given numbers: 7, 21, 27, 28, 35, 49

Check each:

- 7 ÷ 7 = 1 → ✔ multiple
- 21 ÷ 7 = 3 → ✔ multiple
- 27 ÷ 7 ≈ 3.857 → ✘ not a multiple
- 28 ÷ 7 = 4 → ✔ multiple
- 35 ÷ 7 = 5 → ✔ multiple
- 49 ÷ 7 = 7 → ✔ multiple

✔ Circle: 7, 21, 28, 35, 49

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3) Circle the numbers that are factors of 20.

A factor of a number divides it evenly (no remainder).

Factors of 20: Numbers that divide 20 with no remainder.

Check each given number:

- 1 → 20 ÷ 1 = 20 → ✔
- 2 → 20 ÷ 2 = 10 → ✔
- 4 → 20 ÷ 4 = 5 → ✔
- 10 → 20 ÷ 10 = 2 → ✔
- 12 → 20 ÷ 12 ≈ 1.666 → ✘
- 15 → 20 ÷ 15 ≈ 1.333 → ✘
- 20 → 20 ÷ 20 = 1 → ✔

✔ Circle: 1, 2, 4, 10, 20

*(Note: The full list of factors of 20 is 1, 2, 4, 5, 10, 20 — but 5 isn’t in the list, so we only circle those present.)*

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4) Circle the factors of 32.

Factors of 32: 1, 2, 4, 8, 16, 32

Given numbers: 1, 2, 4, 8, 10, 12, 14, 16

Check each:

- 1 → 32 ÷ 1 = 32 → ✔
- 2 → 32 ÷ 2 = 16 → ✔
- 4 → 32 ÷ 4 = 8 → ✔
- 8 → 32 ÷ 8 = 4 → ✔
- 10 → 32 ÷ 10 = 3.2 → ✘
- 12 → 32 ÷ 12 ≈ 2.666 → ✘
- 14 → 32 ÷ 14 ≈ 2.285 → ✘
- 16 → 32 ÷ 16 = 2 → ✔

✔ Circle: 1, 2, 4, 8, 16

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5) I am a multiple of 13. I am also an even number less than 50. Who am I?

First, list multiples of 13 less than 50:

→ 13 × 1 = 13 (odd)
→ 13 × 2 = 26 (even) ✔
→ 13 × 3 = 39 (odd)
→ 13 × 4 = 52 (too big — over 50)

Only 26 fits all conditions: multiple of 13, even, less than 50.

✔ Answer: 26

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6) List down all the factors of the given numbers.

a) 16

Find all numbers that divide 16 evenly:

→ 1 × 16 = 16
→ 2 × 8 = 16
→ 4 × 4 = 16

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

✔ Answer: 1, 2, 4, 8, 16

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b) 42

Find pairs of numbers that multiply to 42:

→ 1 × 42 = 42
→ 2 × 21 = 42
→ 3 × 14 = 42
→ 6 × 7 = 42

So factors are: 1, 2, 3, 6, 7, 14, 21, 42

✔ Answer: 1, 2, 3, 6, 7, 14, 21, 42

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## ✔ Final Answers Summary:

1)
a) 5, 10
b) 12, 24
c) 4, 8
d) 18, 36

2) Circle: 7, 21, 28, 35, 49

3) Circle: 1, 2, 4, 10, 20

4) Circle: 1, 2, 4, 8, 16

5) 26

6)
a) 1, 2, 4, 8, 16
b) 1, 2, 3, 6, 7, 14, 21, 42

Let me know if you’d like this formatted as a worksheet answer key!