Solution: The GCF of 146 and 87 is 1
Methods
How to find the GCF of 146 and 87 using Prime Factorization
One way to find the GCF of 146 and 87 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 146?
What are the Factors of 87?
Here is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 1
And this is the prime factorization of 87:
3
1
×
2
9
1
3^1 × 29^1
3 1 × 2 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 146 and 87 is 1.
Thus, the GCF of 146 and 87 is: 1
How to Find the GCF of 146 and 87 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 146 and 87 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, 146 and 87:
Factors of 146: 1, 2, 73, 146
Factors of 87: 1, 3, 29, 87
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 146 and 87 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 124 and 51?
What is the GCF of 145 and 54?
What is the GCF of 90 and 113?
What is the GCF of 109 and 125?
What is the GCF of 89 and 127?