Solution: The GCF of 48 and 96 is 48
Methods
How to find the GCF of 48 and 96 using Prime Factorization
One way to find the GCF of 48 and 96 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 48?
What are the Factors of 96?
Here is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 3 1
And this is the prime factorization of 96:
2
5
×
3
1
2^5 × 3^1
2 5 × 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 48 and 96 by multiplying all the matching prime factors to get a GCF of 48 and 96 as 36:
Thus, the GCF of 48 and 96 is: 36
How to Find the GCF of 48 and 96 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 48 and 96 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, 48 and 96:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Since 48 is the largest of these common factors, the GCF of 48 and 96 would be 48.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 96 and 42?
What is the GCF of 20 and 130?
What is the GCF of 61 and 86?
What is the GCF of 83 and 52?
What is the GCF of 49 and 136?