Factors and Multiples Worksheet - Free Printable

Let's solve each problem step by step and explain the reasoning.

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1) Circle the numbers below which are multiples of 4:

Numbers:
22, 34, 32, 28, 14, 41, 44

A number is a multiple of 4 if it can be divided by 4 with no remainder.

Check each:
- 22 ÷ 4 = 5.5 → not a multiple
- 34 ÷ 4 = 8.5 → not a multiple
- 32 ÷ 4 = 8 → yes
- 28 ÷ 4 = 7 → yes
- 14 ÷ 4 = 3.5 → not a multiple
- 41 ÷ 4 = 10.25 → not a multiple
- 44 ÷ 4 = 11 → yes

✔ Multiples of 4: 32, 28, 44

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2) Circle the numbers below which are factors of 20:

Numbers:
1, 2, 5, 10, 12, 20, 40

A factor of 20 is a number that divides 20 evenly (no remainder).

Check each:
- 1 → 20 ÷ 1 = 20 → yes
- 2 → 20 ÷ 2 = 10 → yes
- 5 → 20 ÷ 5 = 4 → yes
- 10 → 20 ÷ 10 = 2 → yes
- 12 → 20 ÷ 12 ≈ 1.67 → no
- 20 → 20 ÷ 20 = 1 → yes
- 40 → 20 ÷ 40 = 0.5 → no

✔ Factors of 20: 1, 2, 5, 10, 20

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3) Fill in the table below

| NUMBER | MULTIPLE OF 3 | FACTOR OF 36 |
|--------|----------------|---------------|
| 15 | YES | NO |
| 13 | | |
| 6 | | |
| 10 | | |
| 4 | | |
| 21 | | |
| 12 | | |

#### Step-by-step:

- Multiple of 3? → Check if divisible by 3.
- Factor of 36? → Check if 36 ÷ number is a whole number.

Let’s go row by row:

1. 15: Already filled — YES (15 ÷ 3 = 5), NO (36 ÷ 15 = 2.4 → not whole)
2. 13:
- 13 ÷ 3 ≈ 4.33 → not multiple of 3 → NO
- 36 ÷ 13 ≈ 2.77 → not factor → NO
3. 6:
- 6 ÷ 3 = 2 → YES
- 36 ÷ 6 = 6 → YES
4. 10:
- 10 ÷ 3 ≈ 3.33 → NO
- 36 ÷ 10 = 3.6 → NO
5. 4:
- 4 ÷ 3 ≈ 1.33 → NO
- 36 ÷ 4 = 9 → YES
6. 21:
- 21 ÷ 3 = 7 → YES
- 36 ÷ 21 ≈ 1.71 → NO
7. 12:
- 12 ÷ 3 = 4 → YES
- 36 ÷ 12 = 3 → YES

✔ Updated Table:

| NUMBER | MULTIPLE OF 3 | FACTOR OF 36 |
|--------|----------------|---------------|
| 15 | YES | NO |
| 13 | NO | NO |
| 6 | YES | YES |
| 10 | NO | NO |
| 4 | NO | YES |
| 21 | YES | NO |
| 12 | YES | YES |

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4) Which of the numbers below are prime numbers?

Numbers: 16, 11, 15, 27, 23, 2

A prime number is a number greater than 1 that has only two factors: 1 and itself.

Check each:
- 16 → divisible by 2, 4, 8 → not prime
- 11 → only divisible by 1 and 11 → prime
- 15 → divisible by 3 and 5 → not prime
- 27 → divisible by 3 and 9 → not prime
- 23 → only divisible by 1 and 23 → prime
- 2 → only divisible by 1 and 2 → prime

✔ Prime numbers: 11, 23, 2

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5) Can you find all 6 factors of 32?

We need to list all numbers that divide 32 evenly.

Start from 1 and go up:
- 1 × 32 = 32 → 1, 32
- 2 × 16 = 32 → 2, 16
- 4 × 8 = 32 → 4, 8
- 5? 32 ÷ 5 = 6.4 → no
- 6? 32 ÷ 6 ≈ 5.33 → no
- 7? 32 ÷ 7 ≈ 4.57 → no
- 8 already listed

So factors are: 1, 2, 4, 8, 16, 32

✔ All 6 factors: 1, 2, 4, 8, 16, 32

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

Let’s list multiples of 13:
- 13 × 1 = 13 → odd
- 13 × 2 = 26 → even ✔
- 13 × 3 = 39 → odd
- 13 × 4 = 52 → greater than 50 → too big

Only even multiple of 13 less than 50 is 26

✔ Answer: 26

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✔ Final Answers:

1) Multiples of 4: 32, 28, 44
2) Factors of 20: 1, 2, 5, 10, 20
3) Table filled as shown above
4) Prime numbers: 11, 23, 2
5) Factors of 32: 1, 2, 4, 8, 16, 32
6) Who am I? 26

Let me know if you'd like this formatted as a printable answer sheet!