Solution: The GCF of 31 and 93 is 31
Methods
How to find the GCF of 31 and 93 using Prime Factorization
One way to find the GCF of 31 and 93 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 31?
What are the Factors of 93?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 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 31 and 93 by multiplying all the matching prime factors to get a GCF of 31 and 93 as 961:
Thus, the GCF of 31 and 93 is: 961
How to Find the GCF of 31 and 93 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 31 and 93 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, 31 and 93:
Factors of 31: 1, 31
Factors of 93: 1, 3, 31, 93
When you compare the two lists of factors, you can see that the common factor(s) are 1, 31. Since 31 is the largest of these common factors, the GCF of 31 and 93 would be 31.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 117?
What is the GCF of 28 and 76?
What is the GCF of 129 and 9?
What is the GCF of 78 and 145?
What is the GCF of 116 and 66?