Solution: The GCF of 129 and 40 is 1
Methods
How to find the GCF of 129 and 40 using Prime Factorization
One way to find the GCF of 129 and 40 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 129?
What are the Factors of 40?
Here is the prime factorization of 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 3 1
And this is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 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 129 and 40 is 1.
Thus, the GCF of 129 and 40 is: 1
How to Find the GCF of 129 and 40 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 129 and 40 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, 129 and 40:
Factors of 129: 1, 3, 43, 129
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
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 129 and 40 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 135 and 60?
What is the GCF of 137 and 130?
What is the GCF of 38 and 116?
What is the GCF of 117 and 78?
What is the GCF of 101 and 146?