Factors and Multiples Worksheet - Free Printable

Problem: Solving the Multiples Sheet 4:1

#### Step-by-Step Solution:

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

The multiples of a number are obtained by multiplying that number by integers starting from 1.

| Number | \(1^{\text{st}}\) | \(2^{\text{nd}}\) | \(3^{\text{rd}}\) | \(4^{\text{th}}\) | \(5^{\text{th}}\) | \(6^{\text{th}}\) |
|--------|-------------------|-------------------|-------------------|-------------------|-------------------|-------------------|
| 6 | 6 | 12 | 18 | 24 | 30 | 36 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 |

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2) Which of the groups of numbers below are multiples of 5?

A number is a multiple of 5 if it ends in 0 or 5.

- Group 1: \(4, 10, 13, 17\)
- Multiples of 5: \(10\)

- Group 2: \(7, 27, 37, 47\)
- No multiples of 5.

- Group 3: \(20, 15, 40, 25\)
- Multiples of 5: \(20, 15, 40, 25\)

- Group 4: \(53, 55, 58, 51\)
- Multiples of 5: \(55\)

- Group 5: \(50, 20, 80, 10\)
- Multiples of 5: \(50, 20, 80, 10\)

Answer: Groups 1, 3, 4, and 5 contain multiples of 5.

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3) Which groups of numbers below are multiples of 3?

A number is a multiple of 3 if the sum of its digits is divisible by 3.

- Group 1: \(35, 32, 38, 30\)
- Sum of digits:
- \(35 \rightarrow 3 + 5 = 8\) (not divisible by 3)
- \(32 \rightarrow 3 + 2 = 5\) (not divisible by 3)
- \(38 \rightarrow 3 + 8 = 11\) (not divisible by 3)
- \(30 \rightarrow 3 + 0 = 3\) (divisible by 3)
- Multiples of 3: \(30\)

- Group 2: \(24, 15, 30, 9\)
- Sum of digits:
- \(24 \rightarrow 2 + 4 = 6\) (divisible by 3)
- \(15 \rightarrow 1 + 5 = 6\) (divisible by 3)
- \(30 \rightarrow 3 + 0 = 3\) (divisible by 3)
- \(9 \rightarrow 9\) (divisible by 3)
- Multiples of 3: \(24, 15, 30, 9\)

- Group 3: \(13, 43, 23, 53\)
- Sum of digits:
- \(13 \rightarrow 1 + 3 = 4\) (not divisible by 3)
- \(43 \rightarrow 4 + 3 = 7\) (not divisible by 3)
- \(23 \rightarrow 2 + 3 = 5\) (not divisible by 3)
- \(53 \rightarrow 5 + 3 = 8\) (not divisible by 3)
- No multiples of 3.

- Group 4: \(27, 36, 9, 18\)
- Sum of digits:
- \(27 \rightarrow 2 + 7 = 9\) (divisible by 3)
- \(36 \rightarrow 3 + 6 = 9\) (divisible by 3)
- \(9 \rightarrow 9\) (divisible by 3)
- \(18 \rightarrow 1 + 8 = 9\) (divisible by 3)
- Multiples of 3: \(27, 36, 9, 18\)

- Group 5: \(14, 21, 28, 35\)
- Sum of digits:
- \(14 \rightarrow 1 + 4 = 5\) (not divisible by 3)
- \(21 \rightarrow 2 + 1 = 3\) (divisible by 3)
- \(28 \rightarrow 2 + 8 = 10\) (not divisible by 3)
- \(35 \rightarrow 3 + 5 = 8\) (not divisible by 3)
- Multiples of 3: \(21\)

Answer: Groups 2, 4, and 5 contain multiples of 3.

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4) I am a multiple of 3. I am between 40 and 50. Who could I be?

Multiples of 3 between 40 and 50:
- \(42 = 3 \times 14\)
- \(45 = 3 \times 15\)
- \(48 = 3 \times 16\)

Answer: \(42, 45, 48\)

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5) I am a multiple of 8. I am between 50 and 70. Who could I be?

Multiples of 8 between 50 and 70:
- \(56 = 8 \times 7\)
- \(64 = 8 \times 8\)

Answer: \(56, 64\)

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6) I am a multiple of 6. I am also a multiple of 4. I am less than 30. Who am I?

A number that is a multiple of both 6 and 4 must be a multiple of their least common multiple (LCM). The LCM of 6 and 4 is 12.

Multiples of 12 less than 30:
- \(12 = 12 \times 1\)
- \(24 = 12 \times 2\)

Answer: \(12, 24\)

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7) Write down a multiple of both 7 and 3 that is less than 50.

A number that is a multiple of both 7 and 3 must be a multiple of their least common multiple (LCM). The LCM of 7 and 3 is 21.

Multiples of 21 less than 50:
- \(21 = 21 \times 1\)
- \(42 = 21 \times 2\)

Answer: \(21\) or \(42\)

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Final Answers:

1.
| Number | \(1^{\text{st}}\) | \(2^{\text{nd}}\) | \(3^{\text{rd}}\) | \(4^{\text{th}}\) | \(5^{\text{th}}\) | \(6^{\text{th}}\) |
|--------|-------------------|-------------------|-------------------|-------------------|-------------------|-------------------|
| 6 | 6 | 12 | 18 | 24 | 30 | 36 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 |

2. Groups 1, 3, 4, and 5 contain multiples of 5.

3. Groups 2, 4, and 5 contain multiples of 3.

4. \(42, 45, 48\)

5. \(56, 64\)

6. \(12, 24\)

7. \(21\) or \(42\)

Boxed Final Answer:
\[
\boxed{42, 45, 48; 56, 64; 12, 24; 21 \text{ or } 42}
\]