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GCF of 11 and 16

The gcf of 11 and 16 is the largest positive integer that divides the numbers 11 and 16 without a remainder. Spelled out, it is the greatest common factor of 11 and 16. Here you can find the result for 11 and 16, 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 11 and 16, but also that of three or more integers including eleven and sixteen for example. Keep reading to learn everything about the gcf (11,16) and the terms related to it.

What is the Greatest Common Factor of 11 and 16?

If you just want to know what is the greatest common factor of 11 and 16, it is 1. Usually, this is written as

gcf(11,16) = 1


The gcf of 11 and 16 can be obtained like this:
  • The factors of 11 are 11, 1.
  • The factors of 16 are 16, 8, 4, 2, 1.
  • The common factors of 11 and 16 are 1, intersecting the two sets above.
  • In the intersection factors of 11 ∩ factors of 16 the greatest element is 1.
  • Therefore, the greatest common factor of 11 and 16 is 1.

Taking the above into account you also know how to find all the common factors of 11 and 16, not just the greatest. In the next section we show you how to calculate the gcf of eleven and sixteen by means of two more methods.

How to find the GCF of 11 and 16

The greatest common factor of 11 and 16 can be computed by using the least common multiple aka lcm of 11 and 16. This is the easiest approach:

gcf (11,16) = = 1



Alternatively, the gcf of 11 and 16 can be found using the prime factorization of 11 and 16:
  • The prime factorization of 11 is: 11
  • The prime factorization of 16 is: 2 x 2 x 2 x 2
  • The prime factors and multiplicities 11 and 16 have in common are: 1
  • 1 is the gcf of 11 and 16
  • gcf(11,16) = 1

In any case, the easiest way to compute the result for two numbers like 11 and 16 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 11,16. 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 11 and 16

What is the greatest common factor of 11 and 16 used for? Answer: It is helpful for reducing fractions like 11 / 16. Just divide the nominator as well as the denominator by the gcf (11,16) to reduce the fraction to lowest terms.

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Next, we shed a light on the mathematical properties.

Properties of GCF of 11 and 16

The most important properties of the gcf(11,16) are:

  • Commutative property: gcf(11,16) = gcf(16,11)
  • Associative property: gcf(11,16,n) = gcf(gcf(16,11),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 eleven / sixteen 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