Factors and Multiples Worksheets - Math Monks - Free Printable

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

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1. Write the first five multiples of the following numbers.

Multiples are the products of a number and any whole number (1, 2, 3, ...).

#### a. 4
Multiply 4 by 1, 2, 3, 4, 5:
- 4 × 1 = 4
- 4 × 2 = 8
- 4 × 3 = 12
- 4 × 4 = 16
- 4 × 5 = 20

✔ Answer: 4, 8, 12, 16, 20

#### b. 13
- 13 × 1 = 13
- 13 × 2 = 26
- 13 × 3 = 39
- 13 × 4 = 52
- 13 × 5 = 65

✔ Answer: 13, 26, 39, 52, 65

#### c. 19
- 19 × 1 = 19
- 19 × 2 = 38
- 19 × 3 = 57
- 19 × 4 = 76
- 19 × 5 = 95

✔ Answer: 19, 38, 57, 76, 95

#### d. 9
- 9 × 1 = 9
- 9 × 2 = 18
- 9 × 3 = 27
- 9 × 4 = 36
- 9 × 5 = 45

✔ Answer: 9, 18, 27, 36, 45

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2. Write four common multiples of the following numbers.

Common multiples are numbers that are multiples of both given numbers.

#### a. 4 and 5
List multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ...
List multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...

Common multiples: 20, 40, 60, 80, ...

✔ Answer: 20, 40, 60, 80

#### b. 3 and 6
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...

Common multiples: 6, 12, 18, 24, ...

✔ Answer: 6, 12, 18, 24

#### c. 5 and 10
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
Multiples of 10: 10, 20, 30, 40, 50, ...

Common multiples: 10, 20, 30, 40, ...

✔ Answer: 10, 20, 30, 40

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3. Find all the factors of the following numbers using multiplication method.

The multiplication method means writing the number as a product of two numbers and listing all such pairs.

#### a. 72
We find pairs of numbers that multiply to give 72:

- 1 × 72 = 72 → factors: 1, 72
- 2 × 36 = 72 → factors: 2, 36
- 3 × 24 = 72 → factors: 3, 24
- 4 × 18 = 72 → factors: 4, 18
- 6 × 12 = 72 → factors: 6, 12
- 8 × 9 = 72 → factors: 8, 9
- 9 × 8 = 72 → already listed
So stop here (we’ve passed √72 ≈ 8.5)

Now list all unique factors:
✔ Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

#### b. 98
Find pairs:

- 1 × 98 = 98 → 1, 98
- 2 × 49 = 98 → 2, 49
- 7 × 14 = 98 → 7, 14
- 14 × 7 = 98 → already listed

So factors are:
✔ Answer: 1, 2, 7, 14, 49, 98

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4. Find all the factors of 25 using division method.

Division method: Divide 25 by numbers starting from 1 up to √25 (which is 5), and check if they divide evenly.

- 25 ÷ 1 = 25 → so 1 and 25 are factors
- 25 ÷ 2 = 12.5 → not divisible
- 25 ÷ 3 ≈ 8.33 → no
- 25 ÷ 4 = 6.25 → no
- 25 ÷ 5 = 5 → so 5 is a factor

So factors: 1, 5, 25

✔ Answer: 1, 5, 25

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✔ Final Answers Summary:

#### 1. First five multiples:
a. 4 → 4, 8, 12, 16, 20
b. 13 → 13, 26, 39, 52, 65
c. 19 → 19, 38, 57, 76, 95
d. 9 → 9, 18, 27, 36, 45

#### 2. Four common multiples:
a. 4 and 5 → 20, 40, 60, 80
b. 3 and 6 → 6, 12, 18, 24
c. 5 and 10 → 10, 20, 30, 40

#### 3. All factors using multiplication method:
a. 72 → 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
b. 98 → 1, 2, 7, 14, 49, 98

#### 4. All factors of 25 using division method:
→ 1, 5, 25

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