Solution: The GCF of 23 and 123 is 1
Methods
How to find the GCF of 23 and 123 using Prime Factorization
One way to find the GCF of 23 and 123 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 23?
What are the Factors of 123?
Here is the prime factorization of 23:
2
3
1
23^1
2 3 1
And this is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 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 23 and 123 is 1.
Thus, the GCF of 23 and 123 is: 1
How to Find the GCF of 23 and 123 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 23 and 123 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, 23 and 123:
Factors of 23: 1, 23
Factors of 123: 1, 3, 41, 123
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 23 and 123 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 145 and 67?
What is the GCF of 44 and 84?
What is the GCF of 51 and 127?
What is the GCF of 55 and 18?
What is the GCF of 12 and 33?