Solution: The GCF of 71 and 116 is 1
Methods
How to find the GCF of 71 and 116 using Prime Factorization
One way to find the GCF of 71 and 116 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 71?
What are the Factors of 116?
Here is the prime factorization of 71:
7
1
1
71^1
7 1 1
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 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 71 and 116 is 1.
Thus, the GCF of 71 and 116 is: 1
How to Find the GCF of 71 and 116 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 71 and 116 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, 71 and 116:
Factors of 71: 1, 71
Factors of 116: 1, 2, 4, 29, 58, 116
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 71 and 116 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 132 and 54?
What is the GCF of 9 and 91?
What is the GCF of 19 and 141?
What is the GCF of 46 and 37?
What is the GCF of 45 and 133?