# What Is The Greatest Common Factor Of 6 And 18 ? Gcf Of 6 And 18

The **gcf of 6 and 18** is the largest positive integer that divides the numbers 6 and 18 without a remainder. Spelled out, it is the greatest common factor of 6 and 18. Here you can find the gcf of 6 and 18, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 6 and 18, but also that of three or more integers including six and eighteen for example. Keep reading to learn everything about the gcf (6,18) and the terms related to it.

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## What is the GCF of 6 and 18

If you just want to know *what is the greatest common factor of 6 and 18*, it is **6**. Usually, this is written as**gcf(6,18) = 6**

The gcf of 6 and 18 can be obtained like this:

The factors of 6 are 6, 3, 2, 1. The factors of 18 are 18, 9, 6, 3, 2, 1. The *common* factors of 6 and 18 are 6, 3, 2, 1, intersecting the two sets above. In the intersection factors of 6 ∩ factors of 18 the *greatest* element is 6. Therefore, the **greatest common factor of 6 and 18 is 6**.

Taking the above into account you also know how to find *all* the common factors of 6 and 18, not just the greatest. In the next section we show you how to calculate the gcf of six and eighteen by means of two more methods.

## How to find the GCF of 6 and 18

The greatest common factor of 6 and 18 can be computed by using the least common multiple aka lcm of 6 and 18. This is the easiest approach:

gcf (6,18) = frac{6 imes 18}{lcm(6,18)} = frac{108}{18} = 6

Alternatively, the gcf of 6 and 18 can be found using the prime factorization of 6 and 18:

The prime factorization of 6 is: 2 x 3 The prime factorization of 18 is: 2 x 3 x 3 The prime factors and multiplicities 6 and 18 have in common are: 2 x 3 2 x 3 is the gcf of 6 and 18 gcf(6,18) = 6

In any case, the easiest way to compute the gcf of two numbers like 6 and 18 is by using our calculator below. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 6,18. The calculation is conducted automatically.

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## Use of GCF of 6 and 18

What is the greatest common factor of 6 and 18 used for? Answer: It is helpful for reducing fractions like 6 / 18. Just divide the nominator as well as the denominator by the gcf (6,18) to reduce the fraction to lowest terms.

frac{6}{18} = frac{frac{6}{6}}{frac{18}{6}} = frac{1}{3}.

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## Properties of GCF of 6 and 18

The most important properties of the gcf(6,18) are:

Commutative property: gcf(6,18) = gcf(18,6) Associative property: gcf(6,18,n) = gcf(gcf(18,6),n) n

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The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.

To sum up, the gcf of 6 and 18 is 6. In common notation: gcf (6,18) = 6.

If you have been searching for gcf 6 and 18 or gcf 6 18 then you have come to the correct page, too. The same is the true if you typed gcf for 6 and 18 in your favorite search engine.

Note that you can find the greatest common factor of many integer pairs including six / eighteen by using the search form in the sidebar of this page.

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