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GCF of 6 and 84

The gcf of 6 and 84 is the largest positive integer that divides the numbers 6 and 84 without a remainder. Spelled out, it is the greatest common factor of 6 and 84. Here you can find the result for 6 and 84, along with a total of three methods for computing it.


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This Greatest Common Factor Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 6 and 84, but also that of three or more integers including six and eighty-four for example. Keep reading to learn everything about the gcf (6,84) and the terms related to it.

What is the Greatest Common Factor of 6 and 84?

If you just want to know what is the greatest common factor of 6 and 84, it is 6. Usually, this is written as

gcf(6,84) = 6


The gcf of 6 and 84 can be obtained like this:
  • The factors of 6 are 6, 3, 2, 1.
  • The factors of 84 are 84, 42, 28, 21, 14, 12, 7, 6, 4, 3, 2, 1.
  • The common factors of 6 and 84 are 6, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 6 ∩ factors of 84 the greatest element is 6.
  • Therefore, the greatest common factor of 6 and 84 is 6.

Taking the above into account you also know how to find all the common factors of 6 and 84, not just the greatest. In the next section we show you how to calculate the gcf of six and eighty-four by means of two more methods.

How to find the GCF of 6 and 84

The greatest common factor of 6 and 84 can be computed by using the least common multiple aka lcm of 6 and 84. This is the easiest approach:

gcf (6,84) = = 6



Alternatively, the gcf of 6 and 84 can be found using the prime factorization of 6 and 84:
  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • The prime factors and multiplicities 6 and 84 have in common are: 2 x 3
  • 2 x 3 is the gcf of 6 and 84
  • gcf(6,84) = 6

In any case, the easiest way to compute the result for two numbers like 6 and 84 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 6,84. 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 6 and 84

What is the greatest common factor of 6 and 84 used for? Answer: It is helpful for reducing fractions like 6 / 84. Just divide the nominator as well as the denominator by the gcf (6,84) to reduce the fraction to lowest terms.

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Next, we shed a light on the mathematical properties.

Properties of GCF of 6 and 84

The most important properties of the gcf(6,84) are:

  • Commutative property: gcf(6,84) = gcf(84,6)
  • Associative property: gcf(6,84,n) = gcf(gcf(84,6),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 six / eighty-four by using the search form in the sidebar of this page.

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