Solution: The GCF of 145 and 28 is 1
Methods
How to find the GCF of 145 and 28 using Prime Factorization
One way to find the GCF of 145 and 28 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 145?
What are the Factors of 28?
Here is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 1
And this is the prime factorization of 28:
2
2
×
7
1
2^2 × 7^1
2 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 145 and 28 is 1.
Thus, the GCF of 145 and 28 is: 1
How to Find the GCF of 145 and 28 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 145 and 28 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, 145 and 28:
Factors of 145: 1, 5, 29, 145
Factors of 28: 1, 2, 4, 7, 14, 28
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 145 and 28 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 113 and 71?
What is the GCF of 136 and 133?
What is the GCF of 110 and 11?
What is the GCF of 90 and 92?
What is the GCF of 102 and 36?