To solve the problem of finding the greatest common factor (GCF) for each pair of numbers, we need to follow these steps:
Step 1: Find the factors of each number.
-
Factors of a number are all the integers that divide the number without leaving a remainder.
Step 2: Identify the common factors.
- Compare the factors of each pair of numbers and find the factors that are common to both.
Step 3: Determine the greatest common factor.
- From the common factors, select the largest one. This is the GCF.
Let's solve each pair step by step:
---
Pair 1: \( \text{GCF}(12, 9) \)
#### Factors of 12:
\[ 1, 2, 3, 4, 6, 12 \]
#### Factors of 9:
\[ 1, 3, 9 \]
#### Common Factors:
\[ 1, 3 \]
#### Greatest Common Factor:
\[ \text{GCF}(12, 9) = 3 \]
---
Pair 2: \( \text{GCF}(12, 20) \)
#### Factors of 12:
\[ 1, 2, 3, 4, 6, 12 \]
#### Factors of 20:
\[ 1, 2, 4, 5, 10, 20 \]
#### Common Factors:
\[ 1, 2, 4 \]
#### Greatest Common Factor:
\[ \text{GCF}(12, 20) = 4 \]
---
Pair 3: \( \text{GCF}(12, 30) \)
#### Factors of 12:
\[ 1, 2, 3, 4, 6, 12 \]
#### Factors of 30:
\[ 1, 2, 3, 5, 6, 10, 15, 30 \]
#### Common Factors:
\[ 1, 2, 3, 6 \]
#### Greatest Common Factor:
\[ \text{GCF}(12, 30) = 6 \]
---
Pair 4: \( \text{GCF}(12, 22) \)
#### Factors of 12:
\[ 1, 2, 3, 4, 6, 12 \]
#### Factors of 22:
\[ 1, 2, 11, 22 \]
#### Common Factors:
\[ 1, 2 \]
#### Greatest Common Factor:
\[ \text{GCF}(12, 22) = 2 \]
---
Pair 5: \( \text{GCF}(12, 77) \)
#### Factors of 12:
\[ 1, 2, 3, 4, 6, 12 \]
#### Factors of 77:
\[ 1, 7, 11, 77 \]
#### Common Factors:
\[ 1 \]
#### Greatest Common Factor:
\[ \text{GCF}(12, 77) = 1 \]
---
Pair 6: \( \text{GCF}(27, 25) \)
#### Factors of 27:
\[ 1, 3, 9, 27 \]
#### Factors of 25:
\[ 1, 5, 25 \]
#### Common Factors:
\[ 1 \]
#### Greatest Common Factor:
\[ \text{GCF}(27, 25) = 1 \]
---
Final Answers:
\[
\begin{aligned}
&\text{GCF}(12, 9) = 3 \\
&\text{GCF}(12, 20) = 4 \\
&\text{GCF}(12, 30) = 6 \\
&\text{GCF}(12, 22) = 2 \\
&\text{GCF}(12, 77) = 1 \\
&\text{GCF}(27, 25) = 1 \\
\end{aligned}
\]
Boxed Final Answer:
\[
\boxed{3, 4, 6, 2, 1, 1}
\]
Parent Tip: Review the logic above to help your child master the concept of factor worksheets.
