Solution: The GCF of 128 and 24 is 8
Methods
How to find the GCF of 128 and 24 using Prime Factorization
One way to find the GCF of 128 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 128?
What are the Factors of 24?
Here is the prime factorization of 128:
2
7
2^7
2 7
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 128 and 24 by multiplying all the matching prime factors to get a GCF of 128 and 24 as 4:
Thus, the GCF of 128 and 24 is: 4
How to Find the GCF of 128 and 24 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 128 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, 128 and 24:
Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
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, 4, 8. Since 8 is the largest of these common factors, the GCF of 128 and 24 would be 8.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 90 and 5?
What is the GCF of 149 and 34?
What is the GCF of 144 and 101?
What is the GCF of 102 and 66?
What is the GCF of 37 and 38?