Solution: The GCF of 106 and 57 is 1
Methods
How to find the GCF of 106 and 57 using Prime Factorization
One way to find the GCF of 106 and 57 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 57?
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 57:
3
1
×
1
9
1
3^1 × 19^1
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 106 and 57 is 1.
Thus, the GCF of 106 and 57 is: 1
How to Find the GCF of 106 and 57 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 106 and 57 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 57:
Factors of 106: 1, 2, 53, 106
Factors of 57: 1, 3, 19, 57
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 57 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 33 and 142?
What is the GCF of 56 and 109?
What is the GCF of 131 and 110?
What is the GCF of 91 and 41?
What is the GCF of 36 and 9?