Factors and Multiples Revision Worksheet | Twinkl Maths - Free Printable

Let's solve the "Factors and Multiples Revision" worksheet step by step. I'll go through each section, explain how to solve it, and provide the correct answers.

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Page 1: Factors and Multiples

#### Section 1: Circle the factors of 18
We are given a list of numbers:
```
2 3 6 5
1 15 7 10
```

We need to circle the factors of 18.

Step-by-step:
- A factor of 18 is a number that divides 18 evenly (no remainder).
- Let’s check each number:
- 2 → 18 ÷ 2 = 9 → ✔ Yes
- 3 → 18 ÷ 3 = 6 → ✔ Yes
- 6 → 18 ÷ 6 = 3 → ✔ Yes
- 5 → 18 ÷ 5 = 3.6 → ✘ No
- 1 → 18 ÷ 1 = 18 → ✔ Yes
- 15 → 18 ÷ 15 = 1.2 → ✘ No
- 7 → 18 ÷ 7 ≈ 2.57 → ✘ No
- 10 → 18 ÷ 10 = 1.8 → ✘ No

✔ Factors of 18: 1, 2, 3, 6

> So circle: 1, 2, 3, 6

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#### Section 2: Select the common factor for 10 and 15

Numbers:
- 10 → factors: 1, 2, 5, 10
- 15 → factors: 1, 3, 5, 15

Common factors: 1 and 5
But we're asked to select from the options shown:

```
12 5 9 10
```

Only 5 is a common factor of both 10 and 15.

✔ Answer: 5

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#### Section 3: Select the common factor for 36 and 24

- 36 → factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 24 → factors: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 4, 6, 12

Now look at the choices:

```
10 6 12 4 44
```

Which of these are common factors?
→ 6, 12, 4 are all common factors.

So, select 6, 12, and 4.

✔ Answers: 6, 12, 4

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#### Section 4: Select the common factor for 30 and 18

- 30 → factors: 1, 2, 3, 5, 6, 10, 15, 30
- 18 → factors: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6

Choices:

```
30 9 5 6 18
```

Which are common?
→ 6 is common.
9 and 18 are not factors of 30.
30 is not a factor of 18.
5 is not a factor of 18.

So only 6 is a common factor.

✔ Answer: 6

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Page 2: Factors and Multiples Revision

#### Section 1: Circle the factors

We have four boxes with lists of numbers. We must circle the actual factors of the given number.

---

##### Factors of 18
List:
`2 3 6 5`
`1 15 7 10`

We already did this above.

✔ Circle: 1, 2, 3, 6

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##### Factors of 20
List:
`2 4 6 5`
`20 15 1 10`

Check which divide 20 evenly:

- 2 → 20 ÷ 2 = 10 → ✔
- 4 → 20 ÷ 4 = 5 → ✔
- 6 → 20 ÷ 6 ≈ 3.33 → ✘
- 5 → 20 ÷ 5 = 4 → ✔
- 20 → 20 ÷ 20 = 1 → ✔
- 15 → 20 ÷ 15 ≈ 1.33 → ✘
- 1 → 20 ÷ 1 = 20 → ✔
- 10 → 20 ÷ 10 = 2 → ✔

✔ Circle: 2, 4, 5, 20, 1, 10

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##### Factors of 48
List:
`2 7 4 6`
`25 8 10 12`

Check:

- 2 → 48 ÷ 2 = 24 → ✔
- 7 → 48 ÷ 7 ≈ 6.85 → ✘
- 4 → 48 ÷ 4 = 12 → ✔
- 6 → 48 ÷ 6 = 8 → ✔
- 25 → 48 ÷ 25 = 1.92 → ✘
- 8 → 48 ÷ 8 = 6 → ✔
- 10 → 48 ÷ 10 = 4.8 → ✘
- 12 → 48 ÷ 12 = 4 → ✔

✔ Circle: 2, 4, 6, 8, 12

---

##### Factors of 36
List:
`2 8 4 6`
`27 12 18 15`

Check:

- 2 → 36 ÷ 2 = 18 → ✔
- 8 → 36 ÷ 8 = 4.5 → ✘
- 4 → 36 ÷ 4 = 9 → ✔
- 6 → 36 ÷ 6 = 6 → ✔
- 27 → 36 ÷ 27 ≈ 1.33 → ✘
- 12 → 36 ÷ 12 = 3 → ✔
- 18 → 36 ÷ 18 = 2 → ✔
- 15 → 36 ÷ 15 = 2.4 → ✘

✔ Circle: 2, 4, 6, 12, 18

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#### Section 2: Write the next four multiples

We’re given starting numbers and need to write the next four multiples after them.

Multiples are formed by multiplying the number by 1, 2, 3, 4, ...

Let’s go one by one.

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##### 6 → 12, ____, ____, ____, ____

- 6 × 1 = 6
- 6 × 2 = 12 ← given
- 6 × 3 = 18
- 6 × 4 = 24
- 6 × 5 = 30
- 6 × 6 = 36

So next four after 12: 18, 24, 30, 36

✔ Answer: 18, 24, 30, 36

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##### 18 → ____, ____, ____, ____

Start from 18 (which is 18 × 1)

Next:
- 18 × 2 = 36
- 18 × 3 = 54
- 18 × 4 = 72
- 18 × 5 = 90

✔ Answer: 36, 54, 72, 90

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##### 27 → ____, ____, ____, ____

- 27 × 1 = 27
- 27 × 2 = 54
- 27 × 3 = 81
- 27 × 4 = 108
- 27 × 5 = 135

So next four after 27: 54, 81, 108, 135

✔ Answer: 54, 81, 108, 135

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##### 36 → ____, ____, ____, ____

- 36 × 1 = 36
- 36 × 2 = 72
- 36 × 3 = 108
- 36 × 4 = 144
- 36 × 5 = 180

✔ Answer: 72, 108, 144, 180

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##### 21 → ____, ____, ____, ____

- 21 × 1 = 21
- 21 × 2 = 42
- 21 × 3 = 63
- 21 × 4 = 84
- 21 × 5 = 105

✔ Answer: 42, 63, 84, 105

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##### 24 → ____, ____, ____, ____

- 24 × 1 = 24
- 24 × 2 = 48
- 24 × 3 = 72
- 24 × 4 = 96
- 24 × 5 = 120

✔ Answer: 48, 72, 96, 120

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##### 35 → ____, ____, ____, ____

- 35 × 1 = 35
- 35 × 2 = 70
- 35 × 3 = 105
- 35 × 4 = 140
- 35 × 5 = 175

✔ Answer: 70, 105, 140, 175

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✔ Final Summary of Answers

#### Page 1:
- Factors of 18: Circle 1, 2, 3, 6
- Common factor of 10 and 15: 5
- Common factors of 36 and 24: 6, 12, 4
- Common factor of 30 and 18: 6

#### Page 2:
- Factors of 20: Circle 2, 4, 5, 20, 1, 10
- Factors of 48: Circle 2, 4, 6, 8, 12
- Factors of 36: Circle 2, 4, 6, 12, 18

#### Multiples:
| Number | Next Four Multiples |
|--------|---------------------|
| 6 | 18, 24, 30, 36 |
| 18 | 36, 54, 72, 90 |
| 27 | 54, 81, 108, 135 |
| 36 | 72, 108, 144, 180 |
| 21 | 42, 63, 84, 105 |
| 24 | 48, 72, 96, 120 |
| 35 | 70, 105, 140, 175 |

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