Solution: The GCF of 105 and 149 is 1
Methods
How to find the GCF of 105 and 149 using Prime Factorization
One way to find the GCF of 105 and 149 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 149?
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 149:
14
9
1
149^1
14 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 105 and 149 is 1.
Thus, the GCF of 105 and 149 is: 1
How to Find the GCF of 105 and 149 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 149 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 149:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 149: 1, 149
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 149 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 123 and 94?
What is the GCF of 52 and 137?
What is the GCF of 17 and 19?
What is the GCF of 13 and 57?
What is the GCF of 138 and 71?