Solution: The GCF of 126 and 55 is 1
Methods
How to find the GCF of 126 and 55 using Prime Factorization
One way to find the GCF of 126 and 55 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 126?
What are the Factors of 55?
Here is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 7 1
And this is the prime factorization of 55:
5
1
×
1
1
1
5^1 × 11^1
5 1 × 1 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 126 and 55 is 1.
Thus, the GCF of 126 and 55 is: 1
How to Find the GCF of 126 and 55 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 55 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, 126 and 55:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 55: 1, 5, 11, 55
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 126 and 55 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 112 and 127?
What is the GCF of 68 and 96?
What is the GCF of 27 and 114?
What is the GCF of 90 and 19?
What is the GCF of 14 and 40?