Math worksheet focusing on factors and multiples, including exercises with 100 squares and sentence completion.

Let's solve each part of the Factors and Multiples Worksheet step by step.

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1. Write down the first 6 multiples of each of these numbers

We find multiples by multiplying the number by 1, 2, 3, ..., up to 6.

| Number | 1st | 2nd | 3rd | 4th | 5th | 6th |
|--------|-----|-----|-----|-----|-----|-----|
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 |

✔ Explanation:
For example, multiples of 4:
- 4×1 = 4
- 4×2 = 8
- 4×3 = 12
And so on...

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2. Which of the groups of numbers below are multiples of 3?

Check which numbers in each group are divisible by 3 (i.e., sum of digits divisible by 3 or remainder is 0 when divided by 3).

#### Group A: 7, 27, 37, 47
- 7 ÷ 3 = 2.33 → not a multiple
- 27 ÷ 3 = 9 → ✔
- 37 ÷ 3 = 12.33 → no
- 47 ÷ 3 = 15.66 → no
→ Only 27 is a multiple → ✘ Not all are multiples

#### Group B: 9, 12, 24, 27
- 9 ÷ 3 = 3 → ✔
- 12 ÷ 3 = 4 → ✔
- 24 ÷ 3 = 8 → ✔
- 27 ÷ 3 = 9 → ✔
→ All are multiples → ✔ Yes

#### Group C: 15, 18, 21, 24
- 15 ÷ 3 = 5 → ✔
- 18 ÷ 3 = 6 → ✔
- 21 ÷ 3 = 7 → ✔
- 24 ÷ 3 = 8 → ✔
→ All are multiples → ✔ Yes

#### Group D: 10, 15, 20, 30
- 10 ÷ 3 = 3.33 → ✘
- 15 ÷ 3 = 5 → ✔
- 20 ÷ 3 = 6.66 → ✘
- 30 ÷ 3 = 10 → ✔
→ Not all are multiples → ✘

✔ Answer: The groups that are all multiples of 3 are:
> [9, 12, 24, 27] and [15, 18, 21, 24]

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3. Which of the groups of numbers below are multiples of 8?

A number is a multiple of 8 if it’s divisible by 8 (no remainder).

#### Group A: 48, 56, 64, 72
- 48 ÷ 8 = 6 → ✔
- 56 ÷ 8 = 7 → ✔
- 64 ÷ 8 = 8 → ✔
- 72 ÷ 8 = 9 → ✔
→ All are multiples → ✔ Yes

#### Group B: 5, 15, 20, 25
- 5 ÷ 8 = 0.625 → ✘
- 15 ÷ 8 = 1.875 → ✘
- 20 ÷ 8 = 2.5 → ✘
- 25 ÷ 8 = 3.125 → ✘
→ None are multiples → ✘

#### Group C: 16, 24, 32, 40
- 16 ÷ 8 = 2 → ✔
- 24 ÷ 8 = 3 → ✔
- 32 ÷ 8 = 4 → ✔
- 40 ÷ 8 = 5 → ✔
→ All are multiples → ✔ Yes

#### Group D: 9, 12, 24, 27
- 9 ÷ 8 = 1.125 → ✘
- 12 ÷ 8 = 1.5 → ✘
- 24 ÷ 8 = 3 → ✔
- 27 ÷ 8 = 3.375 → ✘
→ Not all → ✘

✔ Answer: The groups that are all multiples of 8 are:
> [48, 56, 64, 72] and [16, 24, 32, 40]

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4. Which of the groups of numbers below are multiples of 2?

A number is a multiple of 2 if it's even (ends in 0, 2, 4, 6, or 8).

#### Group A: 4, 6, 8, 10
All are even → ✔ Yes

#### Group B: 7, 14, 21, 28
- 7 → odd → ✘
- 14 → even → ✔
- 21 → odd → ✘
- 28 → even → ✔
→ Not all → ✘

#### Group C: 20, 30, 40, 50
All end in 0 → even → ✔ Yes

#### Group D: 20, 22, 24, 26
All even → ✔ Yes

✔ Answer: The groups that are all multiples of 2 are:
> [4, 6, 8, 10], [20, 30, 40, 50], and [20, 22, 24, 26]

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✔ Final Answers:

#### 1. First 6 multiples:
| Number | 1st | 2nd | 3rd | 4th | 5th | 6th |
|--------|-----|-----|-----|-----|-----|-----|
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 |

#### 2. Multiples of 3:
✔ [9, 12, 24, 27] and [15, 18, 21, 24]

#### 3. Multiples of 8:
✔ [48, 56, 64, 72] and [16, 24, 32, 40]

#### 4. Multiples of 2:
✔ [4, 6, 8, 10], [20, 30, 40, 50], and [20, 22, 24, 26]

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