Solution: The GCF of 117 and 41 is 1
Methods
How to find the GCF of 117 and 41 using Prime Factorization
One way to find the GCF of 117 and 41 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 117?
What are the Factors of 41?
Here is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 1
And this is the prime factorization of 41:
4
1
1
41^1
4 1 1
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 117 and 41 is 1.
Thus, the GCF of 117 and 41 is: 1
How to Find the GCF of 117 and 41 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 117 and 41 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, 117 and 41:
Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 41: 1, 41
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 117 and 41 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 65 and 109?
What is the GCF of 83 and 96?
What is the GCF of 105 and 14?
What is the GCF of 104 and 99?
What is the GCF of 108 and 40?