Solution: The GCF of 120 and 36 is 12
Methods
How to find the GCF of 120 and 36 using Prime Factorization
One way to find the GCF of 120 and 36 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 36?
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 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
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 36 by multiplying all the matching prime factors to get a GCF of 120 and 36 as 36:
Thus, the GCF of 120 and 36 is: 36
How to Find the GCF of 120 and 36 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 and 36 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 36:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 120 and 36 would be 12.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 110 and 21?
What is the GCF of 90 and 14?
What is the GCF of 78 and 18?
What is the GCF of 99 and 48?
What is the GCF of 81 and 124?