Solution: The GCF of 123 and 49 is 1
Methods
How to find the GCF of 123 and 49 using Prime Factorization
One way to find the GCF of 123 and 49 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 49?
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 49:
7
2
7^2
7 2
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 49 is 1.
Thus, the GCF of 123 and 49 is: 1
How to Find the GCF of 123 and 49 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 49 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 49:
Factors of 123: 1, 3, 41, 123
Factors of 49: 1, 7, 49
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 49 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 114 and 75?
What is the GCF of 58 and 121?
What is the GCF of 125 and 51?
What is the GCF of 136 and 108?
What is the GCF of 45 and 124?