Greatest Common Factors Worksheets - 15 Worksheets Library - Free Printable
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Step-by-step solution for: Greatest Common Factors Worksheets - 15 Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Greatest Common Factors Worksheets - 15 Worksheets Library
To solve the problem of finding the Greatest Common Factor (GCF) for each set of numbers, we will use the method of prime factorization. The GCF is the largest number that divides all the given numbers without leaving a remainder. Here's how we can solve each pair step by step:
---
- Prime factorization of 40:
\[
40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5
\]
- Prime factorization of 55:
\[
55 = 5 \times 11
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(40, 55) = 5
\]
---
- Prime factorization of 33:
\[
33 = 3 \times 11
\]
- Prime factorization of 44:
\[
44 = 2 \times 2 \times 11 = 2^2 \times 11
\]
- Common factors: The only common factor is \(11\).
- GCF:
\[
\text{GCF}(33, 44) = 11
\]
---
- Prime factorization of 30:
\[
30 = 2 \times 3 \times 5
\]
- Prime factorization of 25:
\[
25 = 5 \times 5 = 5^2
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(30, 25) = 5
\]
---
- Prime factorization of 40:
\[
40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5
\]
- Prime factorization of 18:
\[
18 = 2 \times 3 \times 3 = 2 \times 3^2
\]
- Common factors: The only common factor is \(2\).
- GCF:
\[
\text{GCF}(40, 18) = 2
\]
---
- Prime factorization of 20:
\[
20 = 2 \times 2 \times 5 = 2^2 \times 5
\]
- Prime factorization of 75:
\[
75 = 3 \times 5 \times 5 = 3 \times 5^2
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(20, 75) = 5
\]
---
- Prime factorization of 12:
\[
12 = 2 \times 2 \times 3 = 2^2 \times 3
\]
- Prime factorization of 45:
\[
45 = 3 \times 3 \times 5 = 3^2 \times 5
\]
- Common factors: The only common factor is \(3\).
- GCF:
\[
\text{GCF}(12, 45) = 3
\]
---
- Prime factorization of 24:
\[
24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3
\]
- Prime factorization of 9:
\[
9 = 3 \times 3 = 3^2
\]
- Common factors: The only common factor is \(3\).
- GCF:
\[
\text{GCF}(24, 9) = 3
\]
---
- Prime factorization of 45:
\[
45 = 3 \times 3 \times 5 = 3^2 \times 5
\]
- Prime factorization of 20:
\[
20 = 2 \times 2 \times 5 = 2^2 \times 5
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(45, 20) = 5
\]
---
- Prime factorization of 36:
\[
36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2
\]
- Prime factorization of 18:
\[
18 = 2 \times 3 \times 3 = 2 \times 3^2
\]
- Common factors: The common factors are \(2\) and \(3^2\).
- GCF:
\[
\text{GCF}(36, 18) = 2 \times 3^2 = 18
\]
---
- Prime factorization of 25:
\[
25 = 5 \times 5 = 5^2
\]
- Prime factorization of 35:
\[
35 = 5 \times 7
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(25, 35) = 5
\]
---
\[
\boxed{
\begin{array}{ll}
1. & \text{GCF}(40, 55) = 5 \\
2. & \text{GCF}(33, 44) = 11 \\
3. & \text{GCF}(30, 25) = 5 \\
4. & \text{GCF}(40, 18) = 2 \\
5. & \text{GCF}(20, 75) = 5 \\
6. & \text{GCF}(12, 45) = 3 \\
7. & \text{GCF}(24, 9) = 3 \\
8. & \text{GCF}(45, 20) = 5 \\
9. & \text{GCF}(36, 18) = 18 \\
10. & \text{GCF}(25, 35) = 5 \\
\end{array}
}
\]
---
1. GCF(40, 55)
- Prime factorization of 40:
\[
40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5
\]
- Prime factorization of 55:
\[
55 = 5 \times 11
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(40, 55) = 5
\]
---
2. GCF(33, 44)
- Prime factorization of 33:
\[
33 = 3 \times 11
\]
- Prime factorization of 44:
\[
44 = 2 \times 2 \times 11 = 2^2 \times 11
\]
- Common factors: The only common factor is \(11\).
- GCF:
\[
\text{GCF}(33, 44) = 11
\]
---
3. GCF(30, 25)
- Prime factorization of 30:
\[
30 = 2 \times 3 \times 5
\]
- Prime factorization of 25:
\[
25 = 5 \times 5 = 5^2
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(30, 25) = 5
\]
---
4. GCF(40, 18)
- Prime factorization of 40:
\[
40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5
\]
- Prime factorization of 18:
\[
18 = 2 \times 3 \times 3 = 2 \times 3^2
\]
- Common factors: The only common factor is \(2\).
- GCF:
\[
\text{GCF}(40, 18) = 2
\]
---
5. GCF(20, 75)
- Prime factorization of 20:
\[
20 = 2 \times 2 \times 5 = 2^2 \times 5
\]
- Prime factorization of 75:
\[
75 = 3 \times 5 \times 5 = 3 \times 5^2
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(20, 75) = 5
\]
---
6. GCF(12, 45)
- Prime factorization of 12:
\[
12 = 2 \times 2 \times 3 = 2^2 \times 3
\]
- Prime factorization of 45:
\[
45 = 3 \times 3 \times 5 = 3^2 \times 5
\]
- Common factors: The only common factor is \(3\).
- GCF:
\[
\text{GCF}(12, 45) = 3
\]
---
7. GCF(24, 9)
- Prime factorization of 24:
\[
24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3
\]
- Prime factorization of 9:
\[
9 = 3 \times 3 = 3^2
\]
- Common factors: The only common factor is \(3\).
- GCF:
\[
\text{GCF}(24, 9) = 3
\]
---
8. GCF(45, 20)
- Prime factorization of 45:
\[
45 = 3 \times 3 \times 5 = 3^2 \times 5
\]
- Prime factorization of 20:
\[
20 = 2 \times 2 \times 5 = 2^2 \times 5
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(45, 20) = 5
\]
---
9. GCF(36, 18)
- Prime factorization of 36:
\[
36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2
\]
- Prime factorization of 18:
\[
18 = 2 \times 3 \times 3 = 2 \times 3^2
\]
- Common factors: The common factors are \(2\) and \(3^2\).
- GCF:
\[
\text{GCF}(36, 18) = 2 \times 3^2 = 18
\]
---
10. GCF(25, 35)
- Prime factorization of 25:
\[
25 = 5 \times 5 = 5^2
\]
- Prime factorization of 35:
\[
35 = 5 \times 7
\]
- Common factors: The only common factor is \(5\).
- GCF:
\[
\text{GCF}(25, 35) = 5
\]
---
Final Answers
\[
\boxed{
\begin{array}{ll}
1. & \text{GCF}(40, 55) = 5 \\
2. & \text{GCF}(33, 44) = 11 \\
3. & \text{GCF}(30, 25) = 5 \\
4. & \text{GCF}(40, 18) = 2 \\
5. & \text{GCF}(20, 75) = 5 \\
6. & \text{GCF}(12, 45) = 3 \\
7. & \text{GCF}(24, 9) = 3 \\
8. & \text{GCF}(45, 20) = 5 \\
9. & \text{GCF}(36, 18) = 18 \\
10. & \text{GCF}(25, 35) = 5 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of gcf worksheet 6th grade.
