Solution: The GCF of 25 and 32 is 1
Methods
How to find the GCF of 25 and 32 using Prime Factorization
One way to find the GCF of 25 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 25?
What are the Factors of 32?
Here is the prime factorization of 25:
5
2
5^2
5 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 no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 25 and 32 is 1.
Thus, the GCF of 25 and 32 is: 1
How to Find the GCF of 25 and 32 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 25 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, 25 and 32:
Factors of 25: 1, 5, 25
Factors of 32: 1, 2, 4, 8, 16, 32
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 25 and 32 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 101 and 123?
What is the GCF of 7 and 145?
What is the GCF of 121 and 15?
What is the GCF of 131 and 104?
What is the GCF of 79 and 22?