Solution: The GCF of 128 and 48 is 16
Methods
How to find the GCF of 128 and 48 using Prime Factorization
One way to find the GCF of 128 and 48 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 128?
What are the Factors of 48?
Here is the prime factorization of 128:
2
7
2^7
2 7
And this is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 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 128 and 48 by multiplying all the matching prime factors to get a GCF of 128 and 48 as 4:
Thus, the GCF of 128 and 48 is: 4
How to Find the GCF of 128 and 48 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 128 and 48 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, 128 and 48:
Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8, 16. Since 16 is the largest of these common factors, the GCF of 128 and 48 would be 16.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 70 and 4?
What is the GCF of 8 and 142?
What is the GCF of 118 and 48?
What is the GCF of 51 and 27?
What is the GCF of 92 and 146?