Math Tutor Explains: What is the GCF of 7 and 49?

Need help finding the Greatest Common Factor (GCF)? As your math tutor, when we consider, “What is the GCF of 7 and 49?”, the question we are asking is what would be the largest number that can divide both 7 and 49 exactly, without any remainder left afterwards.

Math Tutor Solution: The GCF of 7 and 49 is 7

Methods

How to find the GCF of 7 and 49 using Prime Factorization

One way to find the GCF of 7 and 49 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 7:

717^1

And this is the prime factorization of 49:

727^2

When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 7 and 49 by multiplying all the matching prime factors to get a GCF of 7 and 49 as 49:

Thus, the GCF of 7 and 49 is: 49

How to Find the GCF of 7 and 49 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 7 and 49 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, 7 and 49:

Factors of 7: 1, 7

Factors of 49: 1, 7, 49

When you compare the two lists of factors, you can see that the common factor(s) are 1, 7. Since 7 is the largest of these common factors, the GCF of 7 and 49 would be 7.

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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