GCF of 84 and 96


The gcf of 84 and 96 is the largest positive integer that divides the numbers 84 and 96 without a remainder. Spelled out, it is the greatest common factor of 84 and 96. Here you can find the gcf of 84 and 96, 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 84 and 96, but also that of three or more integers including eighty-four and ninety-six for example. Keep reading to learn everything about the gcf (84,96) and the terms related to it.

What is the GCF of 84 and 96

If you just want to know what is the greatest common factor of 84 and 96, it is 12. Usually, this is written as

gcf(84,96) = 12

The gcf of 84 and 96 can be obtained like this:

  • The factors of 84 are 84, 42, 28, 21, 14, 12, 7, 6, 4, 3, 2, 1.
  • The factors of 96 are 96, 48, 32, 24, 16, 12, 8, 6, 4, 3, 2, 1.
  • The common factors of 84 and 96 are 12, 6, 4, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 84 ∩ factors of 96 the greatest element is 12.
  • Therefore, the greatest common factor of 84 and 96 is 12.

Taking the above into account you also know how to find all the common factors of 84 and 96, not just the greatest. In the next section we show you how to calculate the gcf of eighty-four and ninety-six by means of two more methods.

How to find the GCF of 84 and 96

The greatest common factor of 84 and 96 can be computed by using the least common multiple aka lcm of 84 and 96. This is the easiest approach:

gcf (84,96) = $\frac{84 \times 96}{lcm(84,96)} = \frac{8064}{672}$ = 12

Alternatively, the gcf of 84 and 96 can be found using the prime factorization of 84 and 96:

  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • The prime factorization of 96 is: 2 x 2 x 2 x 2 x 2 x 3
  • The prime factors and multiplicities 84 and 96 have in common are: 2 x 2 x 3
  • 2 x 2 x 3 is the gcf of 84 and 96
  • gcf(84,96) = 12

In any case, the easiest way to compute the gcf of two numbers like 84 and 96 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 84,96. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 84 and 96

What is the greatest common factor of 84 and 96 used for? Answer: It is helpful for reducing fractions like 84 / 96. Just divide the nominator as well as the denominator by the gcf (84,96) to reduce the fraction to lowest terms.

$\frac{84}{96} = \frac{\frac{84}{12}}{\frac{96}{12}} = \frac{7}{8}$.

Properties of GCF of 84 and 96

The most important properties of the gcf(84,96) are:

  • Commutative property: gcf(84,96) = gcf(96,84)
  • Associative property: gcf(84,96,n) = gcf(gcf(96,84),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 84 and 96 is 12. In common notation: gcf (84,96) = 12.

If you have been searching for gcf 84 and 96 or gcf 84 96 then you have come to the correct page, too. The same is the true if you typed gcf for 84 and 96 in your favorite search engine.

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

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Posted in Greatest Common Factor
One comment on “GCF of 18 and 42
  1. ennessiah says:

    Very good notes

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