Solution: The GCF of 53 and 138 is 1
Methods
How to find the GCF of 53 and 138 using Prime Factorization
One way to find the GCF of 53 and 138 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 53?
What are the Factors of 138?
Here is the prime factorization of 53:
5
3
1
53^1
5 3 1
And this 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
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 53 and 138 is 1.
Thus, the GCF of 53 and 138 is: 1
How to Find the GCF of 53 and 138 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 53 and 138 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, 53 and 138:
Factors of 53: 1, 53
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
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 53 and 138 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 50 and 118?
What is the GCF of 77 and 116?
What is the GCF of 75 and 139?
What is the GCF of 105 and 112?
What is the GCF of 1 and 5?