Solution: The GCF of 113 and 60 is 1
Methods
How to find the GCF of 113 and 60 using Prime Factorization
One way to find the GCF of 113 and 60 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 113?
What are the Factors of 60?
Here is the prime factorization of 113:
11
3
1
113^1
11 3 1
And this is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 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 113 and 60 is 1.
Thus, the GCF of 113 and 60 is: 1
How to Find the GCF of 113 and 60 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 113 and 60 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, 113 and 60:
Factors of 113: 1, 113
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
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 113 and 60 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 14 and 125?
What is the GCF of 111 and 25?
What is the GCF of 65 and 135?
What is the GCF of 130 and 63?
What is the GCF of 140 and 80?