The **gcf of 40 and 60** is the largest positive integer that divides the numbers 40 and 60 without a remainder. Spelled out, it is the greatest common factor of 40 and 60. Here you can find the gcf of 40 and 60, 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 40 and 60, but also that of three or more integers including forty and sixty for example. Keep reading to learn everything about the gcf (40,60) and the terms related to it.

## What is the GCF of 40 and 60

If you just want to know *what is the greatest common factor of 40 and 60*, it is **20**. Usually, this is written as

**gcf(40,60) = 20**

The gcf of 40 and 60 can be obtained like this:

- The factors of 40 are 40, 20, 10, 8, 5, 4, 2, 1.
- The factors of 60 are 60, 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1.
- The
*common*factors of 40 and 60 are 20, 10, 5, 4, 2, 1, intersecting the two sets above. - In the intersection factors of 40 ∩ factors of 60 the
*greatest*element is 20. - Therefore, the
**greatest common factor of 40 and 60 is 20**.

Taking the above into account you also know how to find *all* the common factors of 40 and 60, not just the greatest. In the next section we show you how to calculate the gcf of forty and sixty by means of two more methods.

## How to find the GCF of 40 and 60

The greatest common factor of 40 and 60 can be computed by using the least common multiple aka lcm of 40 and 60. This is the easiest approach:

Alternatively, the gcf of 40 and 60 can be found using the prime factorization of 40 and 60:

- The prime factorization of 40 is: 2 x 2 x 2 x 5
- The prime factorization of 60 is: 2 x 2 x 3 x 5
- The prime factors and multiplicities 40 and 60 have in common are: 2 x 2 x 5
- 2 x 2 x 5 is the gcf of 40 and 60
- gcf(40,60) = 20

In any case, the easiest way to compute the gcf of two numbers like 40 and 60 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 40,60. The calculation is conducted automatically.

## Use of GCF of 40 and 60

What is the greatest common factor of 40 and 60 used for? Answer: It is helpful for reducing fractions like 40 / 60. Just divide the nominator as well as the denominator by the gcf (40,60) to reduce the fraction to lowest terms.

$\frac{40}{60} = \frac{\frac{40}{20}}{\frac{60}{20}} = \frac{2}{3}$.

## Properties of GCF of 40 and 60

The most important properties of the gcf(40,60) are:

- Commutative property: gcf(40,60) = gcf(60,40)
- Associative property: gcf(40,60,n) = gcf(gcf(60,40),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

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 40 and 60 is 20. In common notation: gcf (40,60) = 20.

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

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