Solution: The GCF of 120 and 89 is 1
Methods
How to find the GCF of 120 and 89 using Prime Factorization
One way to find the GCF of 120 and 89 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 120?
What are the Factors of 89?
Here is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 1
And this is the prime factorization of 89:
8
9
1
89^1
8 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 120 and 89 is 1.
Thus, the GCF of 120 and 89 is: 1
How to Find the GCF of 120 and 89 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 and 89 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, 120 and 89:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 89: 1, 89
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 120 and 89 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 102 and 134?
What is the GCF of 47 and 87?
What is the GCF of 57 and 40?
What is the GCF of 72 and 86?
What is the GCF of 74 and 22?