Solution: The GCF of 75 and 119 is 1
Methods
How to find the GCF of 75 and 119 using Prime Factorization
One way to find the GCF of 75 and 119 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 75?
What are the Factors of 119?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
And this is the prime factorization of 119:
7
1
×
1
7
1
7^1 × 17^1
7 1 × 1 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 75 and 119 is 1.
Thus, the GCF of 75 and 119 is: 1
How to Find the GCF of 75 and 119 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 119 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, 75 and 119:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 119: 1, 7, 17, 119
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 75 and 119 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 52 and 139?
What is the GCF of 64 and 87?
What is the GCF of 37 and 127?
What is the GCF of 135 and 133?
What is the GCF of 149 and 7?