Solution: The GCF of 115 and 106 is 1
Methods
How to find the GCF of 115 and 106 using Prime Factorization
One way to find the GCF of 115 and 106 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 115?
What are the Factors of 106?
Here is the prime factorization of 115:
5
1
×
2
3
1
5^1 × 23^1
5 1 × 2 3 1
And this is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 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 115 and 106 is 1.
Thus, the GCF of 115 and 106 is: 1
How to Find the GCF of 115 and 106 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 115 and 106 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, 115 and 106:
Factors of 115: 1, 5, 23, 115
Factors of 106: 1, 2, 53, 106
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 115 and 106 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 38?
What is the GCF of 105 and 57?
What is the GCF of 112 and 59?
What is the GCF of 80 and 97?
What is the GCF of 95 and 19?