Factors And Multiples Worksheet | Download Free Printables For Kids - Free Printable

Problem Analysis:

The worksheet focuses on understanding factors and multiples. Let's break down each part of the problem and solve it step by step.

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Part 1: Write down the first 6 multiples of each of these numbers

#### Step 1: Understand what a multiple is
A multiple of a number is obtained by multiplying that number by any integer (positive, negative, or zero). For this problem, we are asked to find the first 6 positive multiples of each given number.

#### Step 2: Calculate the multiples
We will calculate the first 6 multiples for each number:

- For 4:
- \( 4 \times 1 = 4 \)
- \( 4 \times 2 = 8 \)
- \( 4 \times 3 = 12 \)
- \( 4 \times 4 = 16 \)
- \( 4 \times 5 = 20 \)
- \( 4 \times 6 = 24 \)

- For 3:
- \( 3 \times 1 = 3 \)
- \( 3 \times 2 = 6 \)
- \( 3 \times 3 = 9 \)
- \( 3 \times 4 = 12 \)
- \( 3 \times 5 = 15 \)
- \( 3 \times 6 = 18 \)

- For 9:
- \( 9 \times 1 = 9 \)
- \( 9 \times 2 = 18 \)
- \( 9 \times 3 = 27 \)
- \( 9 \times 4 = 36 \)
- \( 9 \times 5 = 45 \)
- \( 9 \times 6 = 54 \)

- For 5:
- \( 5 \times 1 = 5 \)
- \( 5 \times 2 = 10 \)
- \( 5 \times 3 = 15 \)
- \( 5 \times 4 = 20 \)
- \( 5 \times 5 = 25 \)
- \( 5 \times 6 = 30 \)

- For 7:
- \( 7 \times 1 = 7 \)
- \( 7 \times 2 = 14 \)
- \( 7 \times 3 = 21 \)
- \( 7 \times 4 = 28 \)
- \( 7 \times 5 = 35 \)
- \( 7 \times 6 = 42 \)

#### Step 3: Fill in the table
The completed table is as follows:

| 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 |

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Part 2: Which of the groups of numbers below are multiples of 3?

#### Step 1: Recall the rule for multiples of 3
A number is a multiple of 3 if the sum of its digits is divisible by 3.

#### Step 2: Check each group
- Group 1: \( 7, 27, 37, 47 \)
- \( 7 \): Sum of digits = 7 (not divisible by 3)
- \( 27 \): Sum of digits = \( 2 + 7 = 9 \) (divisible by 3)
- \( 37 \): Sum of digits = \( 3 + 7 = 10 \) (not divisible by 3)
- \( 47 \): Sum of digits = \( 4 + 7 = 11 \) (not divisible by 3)
- Not all numbers are multiples of 3.

- Group 2: \( 9, 12, 24, 27 \)
- \( 9 \): Sum of digits = 9 (divisible by 3)
- \( 12 \): Sum of digits = \( 1 + 2 = 3 \) (divisible by 3)
- \( 24 \): Sum of digits = \( 2 + 4 = 6 \) (divisible by 3)
- \( 27 \): Sum of digits = \( 2 + 7 = 9 \) (divisible by 3)
- All numbers are multiples of 3.

- Group 3: \( 15, 18, 21, 24 \)
- \( 15 \): Sum of digits = \( 1 + 5 = 6 \) (divisible by 3)
- \( 18 \): Sum of digits = \( 1 + 8 = 9 \) (divisible by 3)
- \( 21 \): Sum of digits = \( 2 + 1 = 3 \) (divisible by 3)
- \( 24 \): Sum of digits = \( 2 + 4 = 6 \) (divisible by 3)
- All numbers are multiples of 3.

- Group 4: \( 10, 15, 20, 30 \)
- \( 10 \): Sum of digits = \( 1 + 0 = 1 \) (not divisible by 3)
- \( 15 \): Sum of digits = \( 1 + 5 = 6 \) (divisible by 3)
- \( 20 \): Sum of digits = \( 2 + 0 = 2 \) (not divisible by 3)
- \( 30 \): Sum of digits = \( 3 + 0 = 3 \) (divisible by 3)
- Not all numbers are multiples of 3.

#### Step 3: Identify the correct groups
The groups where all numbers are multiples of 3 are:
- Group 2: \( 9, 12, 24, 27 \)
- Group 3: \( 15, 18, 21, 24 \)

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Part 3: Which of the groups of numbers below are multiples of 8?

#### Step 1: Recall the rule for multiples of 8
A number is a multiple of 8 if the last three digits of the number form a number that is divisible by 8. For smaller numbers, you can directly check divisibility.

#### Step 2: Check each group
- Group 1: \( 48, 56, 64, 72 \)
- \( 48 \): Divisible by 8
- \( 56 \): Divisible by 8
- \( 64 \): Divisible by 8
- \( 72 \): Divisible by 8
- All numbers are multiples of 8.

- Group 2: \( 5, 15, 20, 25 \)
- \( 5 \): Not divisible by 8
- \( 15 \): Not divisible by 8
- \( 20 \): Not divisible by 8
- \( 25 \): Not divisible by 8
- None of the numbers are multiples of 8.

- Group 3: \( 16, 24, 32, 40 \)
- \( 16 \): Divisible by 8
- \( 24 \): Divisible by 8
- \( 32 \): Divisible by 8
- \( 40 \): Divisible by 8
- All numbers are multiples of 8.

- Group 4: \( 9, 12, 24, 27 \)
- \( 9 \): Not divisible by 8
- \( 12 \): Not divisible by 8
- \( 24 \): Divisible by 8
- \( 27 \): Not divisible by 8
- Not all numbers are multiples of 8.

#### Step 3: Identify the correct groups
The groups where all numbers are multiples of 8 are:
- Group 1: \( 48, 56, 64, 72 \)
- Group 3: \( 16, 24, 32, 40 \)

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Part 4: Which of the groups of numbers below are multiples of 2?

#### Step 1: Recall the rule for multiples of 2
A number is a multiple of 2 if it is even (i.e., its last digit is 0, 2, 4, 6, or 8).

#### Step 2: Check each group
- Group 1: \( 4, 6, 8, 10 \)
- \( 4 \): Even
- \( 6 \): Even
- \( 8 \): Even
- \( 10 \): Even
- All numbers are multiples of 2.

- Group 2: \( 7, 14, 21, 28 \)
- \( 7 \): Odd
- \( 14 \): Even
- \( 21 \): Odd
- \( 28 \): Even
- Not all numbers are multiples of 2.

- Group 3: \( 20, 30, 40, 50 \)
- \( 20 \): Even
- \( 30 \): Even
- \( 40 \): Even
- \( 50 \): Even
- All numbers are multiples of 2.

- Group 4: \( 20, 22, 24, 26 \)
- \( 20 \): Even
- \( 22 \): Even
- \( 24 \): Even
- \( 26 \): Even
- All numbers are multiples of 2.

#### Step 3: Identify the correct groups
The groups where all numbers are multiples of 2 are:
- Group 1: \( 4, 6, 8, 10 \)
- Group 3: \( 20, 30, 40, 50 \)
- Group 4: \( 20, 22, 24, 26 \)

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Final Answers:

1. The first 6 multiples of each number are:
- 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. Groups that are multiples of 3:
- \( 9, 12, 24, 27 \)
- \( 15, 18, 21, 24 \)

3. Groups that are multiples of 8:
- \( 48, 56, 64, 72 \)
- \( 16, 24, 32, 40 \)

4. Groups that are multiples of 2:
- \( 4, 6, 8, 10 \)
- \( 20, 30, 40, 50 \)
- \( 20, 22, 24, 26 \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1:} \\
\text{4: } 4, 8, 12, 16, 20, 24 \\
\text{3: } 3, 6, 9, 12, 15, 18 \\
\text{9: } 9, 18, 27, 36, 45, 54 \\
\text{5: } 5, 10, 15, 20, 25, 30 \\
\text{7: } 7, 14, 21, 28, 35, 42 \\
\\
\text{Part 2:} \\
\text{Multiples of 3: } \{9, 12, 24, 27\}, \{15, 18, 21, 24\} \\
\\
\text{Part 3:} \\
\text{Multiples of 8: } \{48, 56, 64, 72\}, \{16, 24, 32, 40\} \\
\\
\text{Part 4:} \\
\text{Multiples of 2: } \{4, 6, 8, 10\}, \{20, 30, 40, 50\}, \{20, 22, 24, 26\}
\end{array}
}
\]