What is the GCF of 106 and 30?

Solution: The GCF of 106 and 30 is 2

Methods

How to find the GCF of 106 and 30 using Prime Factorization

One way to find the GCF of 106 and 30 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 106:

2^1 × 53^1

And this is the prime factorization of 30:

2^1 × 3^1 × 5^1

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 106 and 30 by multiplying all the matching prime factors to get a GCF of 106 and 30 as 4:

Thus, the GCF of 106 and 30 is: 4

How to Find the GCF of 106 and 30 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 106 and 30 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, 106 and 30:

Factors of 106: 1, 2, 53, 106

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 106 and 30 would be 2.

Find the GCF of Other Number Pairs

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

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