Solution: The GCF of 106 and 127 is 1
Methods
How to find the GCF of 106 and 127 using Prime Factorization
One way to find the GCF of 106 and 127 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 106?
What are the Factors of 127?
Here is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 1
And this is the prime factorization of 127:
12
7
1
127^1
12 7 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 106 and 127 is 1.
Thus, the GCF of 106 and 127 is: 1
How to Find the GCF of 106 and 127 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 106 and 127 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, 106 and 127:
Factors of 106: 1, 2, 53, 106
Factors of 127: 1, 127
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 106 and 127 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 113 and 82?
What is the GCF of 2 and 43?
What is the GCF of 54 and 70?
What is the GCF of 147 and 107?
What is the GCF of 8 and 75?