Multiples and Factors Worksheets - 25 Interactive, Printable ... - Free Printable

Problem Analysis:

The worksheet provided focuses on factors, common factors, and the greatest common factor (GCF). Let's break down each section and solve the problems step by step.

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Section 1: List at least 3 factors for each number

#### Step-by-Step Solution:
1. 16: The factors of 16 are numbers that divide 16 evenly. They are:
\( 1, 2, 4, 8, 16 \).
At least 3 factors: \( 1, 2, 4 \).

2. 15: The factors of 15 are:
\( 1, 3, 5, 15 \).
At least 3 factors: \( 1, 3, 5 \).

3. 45: The factors of 45 are:
\( 1, 3, 5, 9, 15, 45 \).
At least 3 factors: \( 1, 3, 5 \).

4. 18: The factors of 18 are:
\( 1, 2, 3, 6, 9, 18 \).
At least 3 factors: \( 1, 2, 3 \).

5. 24: The factors of 24 are:
\( 1, 2, 3, 4, 6, 8, 12, 24 \).
At least 3 factors: \( 1, 2, 3 \).

6. 30: The factors of 30 are:
\( 1, 2, 3, 5, 6, 10, 15, 30 \).
At least 3 factors: \( 1, 2, 3 \).

7. 32: The factors of 32 are:
\( 1, 2, 4, 8, 16, 32 \).
At least 3 factors: \( 1, 2, 4 \).

8. 15: (Repeats from earlier) The factors are:
\( 1, 3, 5, 15 \).
At least 3 factors: \( 1, 3, 5 \).

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Section 2: List at least 2 common factors for each set of numbers

#### Step-by-Step Solution:
1. 16, 20:
- Factors of 16: \( 1, 2, 4, 8, 16 \)
- Factors of 20: \( 1, 2, 4, 5, 10, 20 \)
- Common factors: \( 1, 2, 4 \)
- At least 2 common factors: \( 1, 2 \).

2. 12, 34:
- Factors of 12: \( 1, 2, 3, 4, 6, 12 \)
- Factors of 34: \( 1, 2, 17, 34 \)
- Common factors: \( 1, 2 \)
- At least 2 common factors: \( 1, 2 \).

3. 42, 18:
- Factors of 42: \( 1, 2, 3, 6, 7, 14, 21, 42 \)
- Factors of 18: \( 1, 2, 3, 6, 9, 18 \)
- Common factors: \( 1, 2, 3, 6 \)
- At least 2 common factors: \( 1, 2 \).

4. 18, 14:
- Factors of 18: \( 1, 2, 3, 6, 9, 18 \)
- Factors of 14: \( 1, 2, 7, 14 \)
- Common factors: \( 1, 2 \)
- At least 2 common factors: \( 1, 2 \).

5. 24, 32:
- Factors of 24: \( 1, 2, 3, 4, 6, 8, 12, 24 \)
- Factors of 32: \( 1, 2, 4, 8, 16, 32 \)
- Common factors: \( 1, 2, 4, 8 \)
- At least 2 common factors: \( 1, 2 \).

6. 30, 46:
- Factors of 30: \( 1, 2, 3, 5, 6, 10, 15, 30 \)
- Factors of 46: \( 1, 2, 23, 46 \)
- Common factors: \( 1, 2 \)
- At least 2 common factors: \( 1, 2 \).

7. 38, 50:
- Factors of 38: \( 1, 2, 19, 38 \)
- Factors of 50: \( 1, 2, 5, 10, 25, 50 \)
- Common factors: \( 1, 2 \)
- At least 2 common factors: \( 1, 2 \).

8. 10, 20:
- Factors of 10: \( 1, 2, 5, 10 \)
- Factors of 20: \( 1, 2, 4, 5, 10, 20 \)
- Common factors: \( 1, 2, 5, 10 \)
- At least 2 common factors: \( 1, 2 \).

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Section 3: Find the Greatest Common Factor (GCF) for each set of numbers

#### Step-by-Step Solution:
1. 14, 28:
- Factors of 14: \( 1, 2, 7, 14 \)
- Factors of 28: \( 1, 2, 4, 7, 14, 28 \)
- Common factors: \( 1, 2, 7, 14 \)
- GCF: \( 14 \).

2. 12, 4:
- Factors of 12: \( 1, 2, 3, 4, 6, 12 \)
- Factors of 4: \( 1, 2, 4 \)
- Common factors: \( 1, 2, 4 \)
- GCF: \( 4 \).

3. 42, 6:
- Factors of 42: \( 1, 2, 3, 6, 7, 14, 21, 42 \)
- Factors of 6: \( 1, 2, 3, 6 \)
- Common factors: \( 1, 2, 3, 6 \)
- GCF: \( 6 \).

4. 16, 30:
- Factors of 16: \( 1, 2, 4, 8, 16 \)
- Factors of 30: \( 1, 2, 3, 5, 6, 10, 15, 30 \)
- Common factors: \( 1, 2 \)
- GCF: \( 2 \).

5. 30, 32:
- Factors of 30: \( 1, 2, 3, 5, 6, 10, 15, 30 \)
- Factors of 32: \( 1, 2, 4, 8, 16, 32 \)
- Common factors: \( 1, 2 \)
- GCF: \( 2 \).

6. 80, 40:
- Factors of 80: \( 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 \)
- Factors of 40: \( 1, 2, 4, 5, 8, 10, 20, 40 \)
- Common factors: \( 1, 2, 4, 5, 8, 10, 20, 40 \)
- GCF: \( 40 \).

7. 38, 50:
- Factors of 38: \( 1, 2, 19, 38 \)
- Factors of 50: \( 1, 2, 5, 10, 25, 50 \)
- Common factors: \( 1, 2 \)
- GCF: \( 2 \).

8. 10, 60:
- Factors of 10: \( 1, 2, 5, 10 \)
- Factors of 60: \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \)
- Common factors: \( 1, 2, 5, 10 \)
- GCF: \( 10 \).

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Final Answers:

1. List at least 3 factors for each number:
- 16: \( 1, 2, 4 \)
- 15: \( 1, 3, 5 \)
- 45: \( 1, 3, 5 \)
- 18: \( 1, 2, 3 \)
- 24: \( 1, 2, 3 \)
- 30: \( 1, 2, 3 \)
- 32: \( 1, 2, 4 \)
- 15: \( 1, 3, 5 \)

2. List at least 2 common factors for each set of numbers:
- 16, 20: \( 1, 2 \)
- 12, 34: \( 1, 2 \)
- 42, 18: \( 1, 2 \)
- 18, 14: \( 1, 2 \)
- 24, 32: \( 1, 2 \)
- 30, 46: \( 1, 2 \)
- 38, 50: \( 1, 2 \)
- 10, 20: \( 1, 2 \)

3. Find the Greatest Common Factor (GCF) for each set of numbers:
- 14, 28: \( 14 \)
- 12, 4: \( 4 \)
- 42, 6: \( 6 \)
- 16, 30: \( 2 \)
- 30, 32: \( 2 \)
- 80, 40: \( 40 \)
- 38, 50: \( 2 \)
- 10, 60: \( 10 \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Factors:} \\
16: 1, 2, 4 \\
15: 1, 3, 5 \\
45: 1, 3, 5 \\
18: 1, 2, 3 \\
24: 1, 2, 3 \\
30: 1, 2, 3 \\
32: 1, 2, 4 \\
15: 1, 3, 5 \\
\\
\text{Common Factors:} \\
16, 20: 1, 2 \\
12, 34: 1, 2 \\
42, 18: 1, 2 \\
18, 14: 1, 2 \\
24, 32: 1, 2 \\
30, 46: 1, 2 \\
38, 50: 1, 2 \\
10, 20: 1, 2 \\
\\
\text{GCF:} \\
14, 28: 14 \\
12, 4: 4 \\
42, 6: 6 \\
16, 30: 2 \\
30, 32: 2 \\
80, 40: 40 \\
38, 50: 2 \\
10, 60: 10 \\
\end{array}
}
\]