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GCF of 2 and 7

The gcf of 2 and 7 is the largest positive integer that divides the numbers 2 and 7 without a remainder. Spelled out, it is the greatest common factor of 2 and 7. Here you can find the result for 2 and 7, 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 2 and 7, but also that of three or more integers including two and seven for example. Keep reading to learn everything about the gcf (2,7) and the terms related to it.

What is the Greatest Common Factor of 2 and 7?

If you just want to know what is the greatest common factor of 2 and 7, it is 1. Usually, this is written as

gcf(2,7) = 1


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

Taking the above into account you also know how to find all the common factors of 2 and 7, not just the greatest. In the next section we show you how to calculate the gcf of two and seven by means of two more methods.

How to find the GCF of 2 and 7

The greatest common factor of 2 and 7 can be computed by using the least common multiple aka lcm of 2 and 7. This is the easiest approach:

gcf (2,7) = = 1



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

In any case, the easiest way to compute the result for two numbers like 2 and 7 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 2,7. 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 2 and 7

What is the greatest common factor of 2 and 7 used for? Answer: It is helpful for reducing fractions like 2 / 7. Just divide the nominator as well as the denominator by the gcf (2,7) to reduce the fraction to lowest terms.

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Next, we shed a light on the mathematical properties.

Properties of GCF of 2 and 7

The most important properties of the gcf(2,7) are:

  • Commutative property: gcf(2,7) = gcf(7,2)
  • Associative property: gcf(2,7,n) = gcf(gcf(7,2),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 two / seven 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