Math Tutor Explains: What is the GCF of 144 and 119?

Need help finding the Greatest Common Factor (GCF)? As your math tutor, when we consider, “What is the GCF of 144 and 119?”, the question we are asking is what would be the largest number that can divide both 144 and 119 exactly, without any remainder left afterwards.

Math Tutor Solution: The GCF of 144 and 119 is 1

Methods

How to find the GCF of 144 and 119 using Prime Factorization

One way to find the GCF of 144 and 119 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 144:

24×322^4 × 3^2

And this is the prime factorization of 119:

71×1717^1 × 17^1

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 144 and 119 is 1.

Thus, the GCF of 144 and 119 is: 1

How to Find the GCF of 144 and 119 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 144 and 119 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, 144 and 119:

Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Factors of 119: 1, 7, 17, 119

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 144 and 119 is 1.

Math Tutor Suggests: Find the GCF of Other Number Pairs

Want more practice? Try some of these other GCF problems walkthrough from math tutors:

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