Solution: The GCF of 117 and 37 is 1
Methods
How to find the GCF of 117 and 37 using Prime Factorization
One way to find the GCF of 117 and 37 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 117?
What are the Factors of 37?
Here is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 1
And this is the prime factorization of 37:
3
7
1
37^1
3 7 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 117 and 37 is 1.
Thus, the GCF of 117 and 37 is: 1
How to Find the GCF of 117 and 37 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 117 and 37 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, 117 and 37:
Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 37: 1, 37
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 117 and 37 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 97 and 138?
What is the GCF of 12 and 125?
What is the GCF of 140 and 131?
What is the GCF of 114 and 123?
What is the GCF of 104 and 32?