Solution: The GCF of 103 and 75 is 1
Methods
How to find the GCF of 103 and 75 using Prime Factorization
One way to find the GCF of 103 and 75 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 103?
What are the Factors of 75?
Here is the prime factorization of 103:
10
3
1
103^1
10 3 1
And this is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
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 103 and 75 is 1.
Thus, the GCF of 103 and 75 is: 1
How to Find the GCF of 103 and 75 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 103 and 75 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, 103 and 75:
Factors of 103: 1, 103
Factors of 75: 1, 3, 5, 15, 25, 75
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 103 and 75 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 115 and 94?
What is the GCF of 127 and 15?
What is the GCF of 138 and 18?
What is the GCF of 105 and 25?
What is the GCF of 31 and 96?