Solution: The GCF of 20 and 128 is 4
Methods
How to find the GCF of 20 and 128 using Prime Factorization
One way to find the GCF of 20 and 128 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 20?
What are the Factors of 128?
Here is the prime factorization of 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 5 1
And this is the prime factorization of 128:
2
7
2^7
2 7
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 20 and 128 by multiplying all the matching prime factors to get a GCF of 20 and 128 as 4:
Thus, the GCF of 20 and 128 is: 4
How to Find the GCF of 20 and 128 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 20 and 128 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, 20 and 128:
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
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 20 and 128 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 110 and 67?
What is the GCF of 82 and 2?
What is the GCF of 117 and 76?
What is the GCF of 130 and 74?
What is the GCF of 132 and 15?