MATH SOLVE

2 months ago

Q:
# What is the GCF of 138 and 109?

Accepted Solution

A:

Solution: The GCF of 138 and 109 is 1
Methods
How to find the GCF of 138 and 109 using Prime Factorization
One way to find the GCF of 138 and 109 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 109?
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 109:
10
9
1
109^1
10 9 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 138 and 109 is 1.
Thus, the GCF of 138 and 109 is: 1
How to Find the GCF of 138 and 109 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 109 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 109:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 109: 1, 109
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 138 and 109 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 31 and 13?
What is the GCF of 129 and 141?
What is the GCF of 112 and 53?
What is the GCF of 63 and 75?
What is the GCF of 3 and 33?