What is the GCF of 89 and 74?

Solution: The GCF of 89 and 74 is 1

Methods

How to find the GCF of 89 and 74 using Prime Factorization

One way to find the GCF of 89 and 74 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:

Here is the prime factorization of 89:

89^1

And this is the prime factorization of 74:

2^1 × 37^1

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 89 and 74 is 1.

Thus, the GCF of 89 and 74 is: 1

How to Find the GCF of 89 and 74 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 89 and 74 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, 89 and 74:

Factors of 89: 1, 89

Factors of 74: 1, 2, 37, 74

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 89 and 74 is 1.

Find the GCF of Other Number Pairs

Want more practice? Try some of these other GCF problems:

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