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GCF of 9 and 11

The gcf of 9 and 11 is the largest positive integer that divides the numbers 9 and 11 without a remainder. Spelled out, it is the greatest common factor of 9 and 11. Here you can find the result for 9 and 11, 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 9 and 11, but also that of three or more integers including nine and eleven for example. Keep reading to learn everything about the gcf (9,11) and the terms related to it.

What is the Greatest Common Factor of 9 and 11?

If you just want to know what is the greatest common factor of 9 and 11, it is 1. Usually, this is written as

gcf(9,11) = 1


The gcf of 9 and 11 can be obtained like this:
  • The factors of 9 are 9, 3, 1.
  • The factors of 11 are 11, 1.
  • The common factors of 9 and 11 are 1, intersecting the two sets above.
  • In the intersection factors of 9 ∩ factors of 11 the greatest element is 1.
  • Therefore, the greatest common factor of 9 and 11 is 1.

Taking the above into account you also know how to find all the common factors of 9 and 11, not just the greatest. In the next section we show you how to calculate the gcf of nine and eleven by means of two more methods.

How to find the GCF of 9 and 11

The greatest common factor of 9 and 11 can be computed by using the least common multiple aka lcm of 9 and 11. This is the easiest approach:

gcf (9,11) = = 1



Alternatively, the gcf of 9 and 11 can be found using the prime factorization of 9 and 11:
  • The prime factorization of 9 is: 3 x 3
  • The prime factorization of 11 is: 11
  • The prime factors and multiplicities 9 and 11 have in common are: 1
  • 1 is the gcf of 9 and 11
  • gcf(9,11) = 1

In any case, the easiest way to compute the result for two numbers like 9 and 11 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 9,11. 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 9 and 11

What is the greatest common factor of 9 and 11 used for? Answer: It is helpful for reducing fractions like 9 / 11. Just divide the nominator as well as the denominator by the gcf (9,11) to reduce the fraction to lowest terms.

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Next, we shed a light on the mathematical properties.

Properties of GCF of 9 and 11

The most important properties of the gcf(9,11) are:

  • Commutative property: gcf(9,11) = gcf(11,9)
  • Associative property: gcf(9,11,n) = gcf(gcf(11,9),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 nine / eleven 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