What is the GCF of 53 and 106?

Solution: The GCF of 53 and 106 is 53

Methods

How to find the GCF of 53 and 106 using Prime Factorization

One way to find the GCF of 53 and 106 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 53:

53^1

And this is the prime factorization of 106:

2^1 × 53^1

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 53 and 106 by multiplying all the matching prime factors to get a GCF of 53 and 106 as 2809:

Thus, the GCF of 53 and 106 is: 2809

How to Find the GCF of 53 and 106 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 53 and 106 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, 53 and 106:

Factors of 53: 1, 53

Factors of 106: 1, 2, 53, 106

When you compare the two lists of factors, you can see that the common factor(s) are 1, 53. Since 53 is the largest of these common factors, the GCF of 53 and 106 would be 53.

Find the GCF of Other Number Pairs

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

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