MATH SOLVE

3 months ago

Q:
# What is the GCF of 123 and 56?

Accepted Solution

A:

Solution: The GCF of 123 and 56 is 1
Methods
How to find the GCF of 123 and 56 using Prime Factorization
One way to find the GCF of 123 and 56 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 56?
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 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 7 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 56 is 1.
Thus, the GCF of 123 and 56 is: 1
How to Find the GCF of 123 and 56 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 56 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 56:
Factors of 123: 1, 3, 41, 123
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
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 56 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 41 and 43?
What is the GCF of 30 and 148?
What is the GCF of 22 and 50?
What is the GCF of 120 and 82?
What is the GCF of 65 and 124?