Problem: Find the GCF (Greatest Common Factor) of the given numbers.
The task involves finding the GCF for the following pairs of numbers:
1. \( 12 \) and \( 18 \)
2. \( 6 \) and \( 9 \)
3. \( 10 \) and \( 15 \)
4. \( 7 \) and \( 14 \)
5. \( 18 \) and \( 30 \)
We will solve each pair step by step.
---
####
Step 1: Understand the Method
To find the GCF of two numbers:
1. List all the factors of each number.
2. Identify the common factors.
3. Select the greatest among the common factors.
---
Solution for Each Pair
####
Pair 1: \( 12 \) and \( 18 \)
-
Factors of \( 12 \):
\[
1, 2, 3, 4, 6, 12
\]
-
Factors of \( 18 \):
\[
1, 2, 3, 6, 9, 18
\]
-
Common Factors:
\[
1, 2, 3, 6
\]
-
Greatest Common Factor (GCF):
\[
\text{GCF} = 6
\]
Answer for Pair 1:
\[
\boxed{6}
\]
---
####
Pair 2: \( 6 \) and \( 9 \)
-
Factors of \( 6 \):
\[
1, 2, 3, 6
\]
-
Factors of \( 9 \):
\[
1, 3, 9
\]
-
Common Factors:
\[
1, 3
\]
-
Greatest Common Factor (GCF):
\[
\text{GCF} = 3
\]
Answer for Pair 2:
\[
\boxed{3}
\]
---
####
Pair 3: \( 10 \) and \( 15 \)
-
Factors of \( 10 \):
\[
1, 2, 5, 10
\]
-
Factors of \( 15 \):
\[
1, 3, 5, 15
\]
-
Common Factors:
\[
1, 5
\]
-
Greatest Common Factor (GCF):
\[
\text{GCF} = 5
\]
Answer for Pair 3:
\[
\boxed{5}
\]
---
####
Pair 4: \( 7 \) and \( 14 \)
-
Factors of \( 7 \):
\[
1, 7
\]
-
Factors of \( 14 \):
\[
1, 2, 7, 14
\]
-
Common Factors:
\[
1, 7
\]
-
Greatest Common Factor (GCF):
\[
\text{GCF} = 7
\]
Answer for Pair 4:
\[
\boxed{7}
\]
---
####
Pair 5: \( 18 \) and \( 30 \)
-
Factors of \( 18 \):
\[
1, 2, 3, 6, 9, 18
\]
-
Factors of \( 30 \):
\[
1, 2, 3, 5, 6, 10, 15, 30
\]
-
Common Factors:
\[
1, 2, 3, 6
\]
-
Greatest Common Factor (GCF):
\[
\text{GCF} = 6
\]
Answer for Pair 5:
\[
\boxed{6}
\]
---
Final Answers:
1. \( \text{GCF of } 12 \text{ and } 18 = \boxed{6} \)
2. \( \text{GCF of } 6 \text{ and } 9 = \boxed{3} \)
3. \( \text{GCF of } 10 \text{ and } 15 = \boxed{5} \)
4. \( \text{GCF of } 7 \text{ and } 14 = \boxed{7} \)
5. \( \text{GCF of } 18 \text{ and } 30 = \boxed{6} \)
---
Boxed Final Answer:
\[
\boxed{6, 3, 5, 7, 6}
\]
Parent Tip: Review the logic above to help your child master the concept of find greatest common factor worksheet 4th grade.
