Solution: The GCF of 43 and 126 is 1
Methods
How to find the GCF of 43 and 126 using Prime Factorization
One way to find the GCF of 43 and 126 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 43?
What are the Factors of 126?
Here is the prime factorization of 43:
4
3
1
43^1
4 3 1
And this is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 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 43 and 126 is 1.
Thus, the GCF of 43 and 126 is: 1
How to Find the GCF of 43 and 126 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 43 and 126 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, 43 and 126:
Factors of 43: 1, 43
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
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 43 and 126 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 42 and 68?
What is the GCF of 114 and 58?
What is the GCF of 130 and 82?
What is the GCF of 1 and 104?
What is the GCF of 91 and 34?