Solution: The GCF of 106 and 13 is 1
Methods
How to find the GCF of 106 and 13 using Prime Factorization
One way to find the GCF of 106 and 13 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 13?
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 13:
1
3
1
13^1
1 3 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 13 is 1.
Thus, the GCF of 106 and 13 is: 1
How to Find the GCF of 106 and 13 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 106 and 13 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 13:
Factors of 106: 1, 2, 53, 106
Factors of 13: 1, 13
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 13 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 13 and 25?
What is the GCF of 7 and 16?
What is the GCF of 2 and 137?
What is the GCF of 53 and 91?
What is the GCF of 136 and 150?