Solution: The GCF of 126 and 19 is 1
Methods
How to find the GCF of 126 and 19 using Prime Factorization
One way to find the GCF of 126 and 19 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 19?
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 19:
1
9
1
19^1
1 9 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 19 is 1.
Thus, the GCF of 126 and 19 is: 1
How to Find the GCF of 126 and 19 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 19 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 19:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 19: 1, 19
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 19 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 97 and 116?
What is the GCF of 43 and 23?
What is the GCF of 70 and 58?
What is the GCF of 79 and 38?
What is the GCF of 13 and 132?