Solution: The GCF of 123 and 86 is 1
Methods
How to find the GCF of 123 and 86 using Prime Factorization
One way to find the GCF of 123 and 86 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 123?
What are the Factors of 86?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 86:
2
1
×
4
3
1
2^1 × 43^1
2 1 × 4 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 123 and 86 is 1.
Thus, the GCF of 123 and 86 is: 1
How to Find the GCF of 123 and 86 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 86 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, 123 and 86:
Factors of 123: 1, 3, 41, 123
Factors of 86: 1, 2, 43, 86
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 123 and 86 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 104 and 6?
What is the GCF of 120 and 35?
What is the GCF of 92 and 81?
What is the GCF of 31 and 99?
What is the GCF of 27 and 85?