Solution: The GCF of 71 and 114 is 1
Methods
How to find the GCF of 71 and 114 using Prime Factorization
One way to find the GCF of 71 and 114 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 114?
Here is the prime factorization of 71:
7
1
1
71^1
7 1 1
And this is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 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 114 is 1.
Thus, the GCF of 71 and 114 is: 1
How to Find the GCF of 71 and 114 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 71 and 114 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 114:
Factors of 71: 1, 71
Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114
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 114 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 124 and 73?
What is the GCF of 35 and 89?
What is the GCF of 72 and 20?
What is the GCF of 68 and 86?
What is the GCF of 105 and 54?