Home » Greatest Common Factor » GCF of 32 and 24

GCF of 32 and 24

The gcf of 32 and 24 is the largest positive integer that divides the numbers 32 and 24 without a remainder. Spelled out, it is the greatest common factor of 32 and 24. Here you can find the result for 32 and 24, along with a total of three methods for computing it.


8

This Greatest Common Factor Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 32 and 24, but also that of three or more integers including thirty-two and twenty-four for example. Keep reading to learn everything about the gcf (32,24) and the terms related to it.

What is the Greatest Common Factor of 32 and 24?

If you just want to know what is the greatest common factor of 32 and 24, it is 8. Usually, this is written as

gcf(32,24) = 8


The gcf of 32 and 24 can be obtained like this:
  • The factors of 32 are 32, 16, 8, 4, 2, 1.
  • The factors of 24 are 24, 12, 8, 6, 4, 3, 2, 1.
  • The common factors of 32 and 24 are 8, 4, 2, 1, intersecting the two sets above.
  • In the intersection factors of 32 ∩ factors of 24 the greatest element is 8.
  • Therefore, the greatest common factor of 32 and 24 is 8.

Taking the above into account you also know how to find all the common factors of 32 and 24, not just the greatest. In the next section we show you how to calculate the gcf of thirty-two and twenty-four by means of two more methods.

How to find the GCF of 32 and 24

The greatest common factor of 32 and 24 can be computed by using the least common multiple aka lcm of 32 and 24. This is the easiest approach:

gcf (32,24) = = 8



Alternatively, the gcf of 32 and 24 can be found using the prime factorization of 32 and 24:
  • The prime factorization of 32 is: 2 x 2 x 2 x 2 x 2
  • The prime factorization of 24 is: 2 x 2 x 2 x 3
  • The prime factors and multiplicities 32 and 24 have in common are: 2 x 2 x 2
  • 2 x 2 x 2 is the gcf of 32 and 24
  • gcf(32,24) = 8

In any case, the easiest way to compute the result for two numbers like 32 and 24 is by using our calculator above. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 32,24. The calculation is conducted automatically.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Greatest Common Factor of 32 and 24

What is the greatest common factor of 32 and 24 used for? Answer: It is helpful for reducing fractions like 32 / 24. Just divide the nominator as well as the denominator by the gcf (32,24) to reduce the fraction to lowest terms.

.

Next, we shed a light on the mathematical properties.

Properties of GCF of 32 and 24

The most important properties of the gcf(32,24) are:

  • Commutative property: gcf(32,24) = gcf(24,32)
  • Associative property: gcf(32,24,n) = gcf(gcf(24,32),n)

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

Summary

Note that you can find the greatest common factor of many integer pairs including thirty-two / twenty-four by using the the search form in the sidebar of this page.

Questions and comments are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 32 and 24 has been useful to you, and make sure to bookmark our site.

If you have some time left check out the related sites and resources in the sidebar of this site.

Thanks for your visit.

– Article written by Mark, last updated on August 8th, 2023