Solution: The GCF of 130 and 31 is 1
Methods
How to find the GCF of 130 and 31 using Prime Factorization
One way to find the GCF of 130 and 31 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 130?
What are the Factors of 31?
Here is the prime factorization of 130:
2
1
×
5
1
×
1
3
1
2^1 × 5^1 × 13^1
2 1 × 5 1 × 1 3 1
And this is the prime factorization of 31:
3
1
1
31^1
3 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 130 and 31 is 1.
Thus, the GCF of 130 and 31 is: 1
How to Find the GCF of 130 and 31 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 130 and 31 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, 130 and 31:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
Factors of 31: 1, 31
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 130 and 31 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 89 and 126?
What is the GCF of 143 and 50?
What is the GCF of 113 and 108?
What is the GCF of 116 and 69?
What is the GCF of 150 and 76?