Solution: The GCF of 138 and 103 is 1
Methods
How to find the GCF of 138 and 103 using Prime Factorization
One way to find the GCF of 138 and 103 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 138?
What are the Factors of 103?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 103:
10
3
1
103^1
10 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 138 and 103 is 1.
Thus, the GCF of 138 and 103 is: 1
How to Find the GCF of 138 and 103 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 103 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, 138 and 103:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 103: 1, 103
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 138 and 103 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 109 and 52?
What is the GCF of 87 and 37?
What is the GCF of 38 and 42?
What is the GCF of 44 and 120?
What is the GCF of 119 and 48?