Solution: The GCF of 4 and 32 is 4
Methods
How to find the GCF of 4 and 32 using Prime Factorization
One way to find the GCF of 4 and 32 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 4?
What are the Factors of 32?
Here is the prime factorization of 4:
2
2
2^2
2 2
And this is the prime factorization of 32:
2
5
2^5
2 5
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 4 and 32 by multiplying all the matching prime factors to get a GCF of 4 and 32 as 4:
Thus, the GCF of 4 and 32 is: 4
How to Find the GCF of 4 and 32 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 4 and 32 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, 4 and 32:
Factors of 4: 1, 2, 4
Factors of 32: 1, 2, 4, 8, 16, 32
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 4 and 32 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 108 and 31?
What is the GCF of 125 and 45?
What is the GCF of 2 and 65?
What is the GCF of 96 and 43?
What is the GCF of 51 and 70?