Solution: The GCF of 117 and 122 is 1
Methods
How to find the GCF of 117 and 122 using Prime Factorization
One way to find the GCF of 117 and 122 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 122?
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 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 1 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 122 is 1.
Thus, the GCF of 117 and 122 is: 1
How to Find the GCF of 117 and 122 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 117 and 122 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 122:
Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 122: 1, 2, 61, 122
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 122 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 79 and 57?
What is the GCF of 19 and 36?
What is the GCF of 43 and 55?
What is the GCF of 100 and 38?
What is the GCF of 101 and 37?