Solution: The GCF of 128 and 20 is 4
Methods
How to find the GCF of 128 and 20 using Prime Factorization
One way to find the GCF of 128 and 20 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 20?
Here is the prime factorization of 128:
2
7
2^7
2 7
And this is the prime factorization of 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 5 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 20 by multiplying all the matching prime factors to get a GCF of 128 and 20 as 4:
Thus, the GCF of 128 and 20 is: 4
How to Find the GCF of 128 and 20 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 128 and 20 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 20:
Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
Factors of 20: 1, 2, 4, 5, 10, 20
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 128 and 20 would be 4.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 69 and 47?
What is the GCF of 51 and 58?
What is the GCF of 129 and 119?
What is the GCF of 37 and 25?
What is the GCF of 125 and 17?