Solution: The GCF of 100 and 123 is 1
Methods
How to find the GCF of 100 and 123 using Prime Factorization
One way to find the GCF of 100 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 100?
What are the Factors of 123?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
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 100 and 123 is 1.
Thus, the GCF of 100 and 123 is: 1
How to Find the GCF of 100 and 123 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 100 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, 100 and 123:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
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 100 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 6 and 52?
What is the GCF of 68 and 10?
What is the GCF of 74 and 134?
What is the GCF of 147 and 1?
What is the GCF of 115 and 91?