Solution: The GCF of 120 and 90 is 30
Methods
How to find the GCF of 120 and 90 using Prime Factorization
One way to find the GCF of 120 and 90 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 90?
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 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 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 120 and 90 by multiplying all the matching prime factors to get a GCF of 120 and 90 as 900:
Thus, the GCF of 120 and 90 is: 900
How to Find the GCF of 120 and 90 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 and 90 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 90:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 5, 6, 10, 15, 30. Since 30 is the largest of these common factors, the GCF of 120 and 90 would be 30.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 16 and 81?
What is the GCF of 63 and 34?
What is the GCF of 143 and 7?
What is the GCF of 122 and 142?
What is the GCF of 83 and 115?