MATH SOLVE

3 months ago

Q:
# What is the GCF of 138 and 96?

Accepted Solution

A:

Solution: The GCF of 138 and 96 is 6
Methods
How to find the GCF of 138 and 96 using Prime Factorization
One way to find the GCF of 138 and 96 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 138?
What are the Factors of 96?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 96:
2
5
×
3
1
2^5 × 3^1
2 5 × 3 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 138 and 96 by multiplying all the matching prime factors to get a GCF of 138 and 96 as 36:
Thus, the GCF of 138 and 96 is: 36
How to Find the GCF of 138 and 96 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 96 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 138 and 96:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 138 and 96 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 74 and 78?
What is the GCF of 5 and 122?
What is the GCF of 40 and 49?
What is the GCF of 132 and 148?
What is the GCF of 83 and 55?