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GCF of 14 and 71

The gcf of 14 and 71 is the largest positive integer that divides the numbers 14 and 71 without a remainder. Spelled out, it is the greatest common factor of 14 and 71. Here you can find the result for 14 and 71, 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 14 and 71, but also that of three or more integers including fourteen and seventy-one for example. Keep reading to learn everything about the gcf (14,71) and the terms related to it.

What is the Greatest Common Factor of 14 and 71?

If you just want to know what is the greatest common factor of 14 and 71, it is 1. Usually, this is written as

gcf(14,71) = 1


The gcf of 14 and 71 can be obtained like this:
  • The factors of 14 are 14, 7, 2, 1.
  • The factors of 71 are 71, 1.
  • The common factors of 14 and 71 are 1, intersecting the two sets above.
  • In the intersection factors of 14 ∩ factors of 71 the greatest element is 1.
  • Therefore, the greatest common factor of 14 and 71 is 1.

Taking the above into account you also know how to find all the common factors of 14 and 71, not just the greatest. In the next section we show you how to calculate the gcf of fourteen and seventy-one by means of two more methods.

How to find the GCF of 14 and 71

The greatest common factor of 14 and 71 can be computed by using the least common multiple aka lcm of 14 and 71. This is the easiest approach:

gcf (14,71) = = 1



Alternatively, the gcf of 14 and 71 can be found using the prime factorization of 14 and 71:
  • The prime factorization of 14 is: 2 x 7
  • The prime factorization of 71 is: 71
  • The prime factors and multiplicities 14 and 71 have in common are: 1
  • 1 is the gcf of 14 and 71
  • gcf(14,71) = 1

In any case, the easiest way to compute the result for two numbers like 14 and 71 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 14,71. 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 14 and 71

What is the greatest common factor of 14 and 71 used for? Answer: It is helpful for reducing fractions like 14 / 71. Just divide the nominator as well as the denominator by the gcf (14,71) to reduce the fraction to lowest terms.

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Next, we shed a light on the mathematical properties.

Properties of GCF of 14 and 71

The most important properties of the gcf(14,71) are:

  • Commutative property: gcf(14,71) = gcf(71,14)
  • Associative property: gcf(14,71,n) = gcf(gcf(71,14),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 fourteen / seventy-one 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