Solution: The GCF of 120 and 24 is 24
Methods
How to find the GCF of 120 and 24 using Prime Factorization
One way to find the GCF of 120 and 24 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 24?
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 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 3 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 24 by multiplying all the matching prime factors to get a GCF of 120 and 24 as 36:
Thus, the GCF of 120 and 24 is: 36
How to Find the GCF of 120 and 24 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 and 24 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 24:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 8, 12, 24. Since 24 is the largest of these common factors, the GCF of 120 and 24 would be 24.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 69 and 84?
What is the GCF of 103 and 131?
What is the GCF of 105 and 83?
What is the GCF of 80 and 18?
What is the GCF of 142 and 106?