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GCF of 87 and 68

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The gcf of 87 and 68 is the largest positive integer that divides the numbers 87 and 68 without a remainder. Spelled out, it is the greatest common factor of 87 and 68. Here you can find the gcf of 87 and 68, along with a total of three methods for computing it.


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This Greatest Common Factor Calculator is Really Cool! Click To TweetIn addition, we have a calculator you should check out. Not only can it determine the gcf of 87 and 68, but also that of three or more integers including eighty-seven and sixty-eight for example. Keep reading to learn everything about the gcf (87,68) and the terms related to it.

What is the GCF of 87 and 68

If you just want to know what is the greatest common factor of 87 and 68, it is 1. Usually, this is written as

gcf(87,68) = 1

The gcf of 87 and 68 can be obtained like this:

  • The factors of 87 are 87, 29, 3, 1.
  • The factors of 68 are 68, 34, 17, 4, 2, 1.
  • The common factors of 87 and 68 are 1, intersecting the two sets above.
  • In the intersection factors of 87 ∩ factors of 68 the greatest element is 1.
  • Therefore, the greatest common factor of 87 and 68 is 1.

Taking the above into account you also know how to find all the common factors of 87 and 68, not just the greatest. In the next section we show you how to calculate the gcf of eighty-seven and sixty-eight by means of two more methods.

How to find the GCF of 87 and 68

The greatest common factor of 87 and 68 can be computed by using the least common multiple aka lcm of 87 and 68. This is the easiest approach:

gcf (87,68) = = 1

Alternatively, the gcf of 87 and 68 can be found using the prime factorization of 87 and 68:

  • The prime factorization of 87 is: 3 x 29
  • The prime factorization of 68 is: 2 x 2 x 17
  • The prime factors and multiplicities 87 and 68 have in common are: 1
  • 1 is the gcf of 87 and 68
  • gcf(87,68) = 1

In any case, the easiest way to compute the gcf of two numbers like 87 and 68 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 87,68. The calculation is conducted automatically.

Similar searched terms on our site also include:

Use of GCF of 87 and 68

What is the greatest common factor of 87 and 68 used for? Answer: It is helpful for reducing fractions like 87 / 68. Just divide the nominator as well as the denominator by the gcf (87,68) to reduce the fraction to lowest terms.

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Properties of GCF of 87 and 68

The most important properties of the gcf(87,68) are:

  • Commutative property: gcf(87,68) = gcf(68,87)
  • Associative property: gcf(87,68,n) = gcf(gcf(68,87),n)

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 87 and 68 is 1. In common notation: gcf (87,68) = 1.

If you have been searching for gcf 87 and 68 or gcf 87 68 then you have come to the correct page, too. The same is the true if you typed gcf for 87 and 68 in your favorite search engine.

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

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