Solution: The GCF of 125 and 116 is 1
Methods
How to find the GCF of 125 and 116 using Prime Factorization
One way to find the GCF of 125 and 116 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 125?
What are the Factors of 116?
Here is the prime factorization of 125:
5
3
5^3
5 3
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 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 125 and 116 is 1.
Thus, the GCF of 125 and 116 is: 1
How to Find the GCF of 125 and 116 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 125 and 116 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, 125 and 116:
Factors of 125: 1, 5, 25, 125
Factors of 116: 1, 2, 4, 29, 58, 116
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 125 and 116 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 110 and 142?
What is the GCF of 68 and 137?
What is the GCF of 27 and 53?
What is the GCF of 9 and 10?
What is the GCF of 138 and 104?