Solution: The GCF of 105 and 107 is 1
Methods
How to find the GCF of 105 and 107 using Prime Factorization
One way to find the GCF of 105 and 107 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 105?
What are the Factors of 107?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 107:
10
7
1
107^1
10 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 105 and 107 is 1.
Thus, the GCF of 105 and 107 is: 1
How to Find the GCF of 105 and 107 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 107 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, 105 and 107:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 107: 1, 107
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 105 and 107 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 143 and 135?
What is the GCF of 22 and 23?
What is the GCF of 67 and 60?
What is the GCF of 27 and 74?
What is the GCF of 96 and 147?