Solution: The GCF of 115 and 60 is 5
Methods
How to find the GCF of 115 and 60 using Prime Factorization
One way to find the GCF of 115 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 115?
What are the Factors of 60?
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 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 matching prime factors. You can now find the Greatest Common Factor of 115 and 60 by multiplying all the matching prime factors to get a GCF of 115 and 60 as 25:
Thus, the GCF of 115 and 60 is: 25
How to Find the GCF of 115 and 60 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 115 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, 115 and 60:
Factors of 115: 1, 5, 23, 115
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 common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 115 and 60 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 65 and 58?
What is the GCF of 83 and 109?
What is the GCF of 37 and 43?
What is the GCF of 110 and 144?
What is the GCF of 113 and 107?