GCF of 52 and 65


The gcf of 52 and 65 is the largest positive integer that divides the numbers 52 and 65 without a remainder. Spelled out, it is the greatest common factor of 52 and 65. Here you can find the gcf of 52 and 65, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 52 and 65, but also that of three or more integers including fifty-two and sixty-five for example. Keep reading to learn everything about the gcf (52,65) and the terms related to it.

What is the GCF of 52 and 65

If you just want to know what is the greatest common factor of 52 and 65, it is 13. Usually, this is written as

gcf(52,65) = 13

The gcf of 52 and 65 can be obtained like this:

  • The factors of 52 are 52, 26, 13, 4, 2, 1.
  • The factors of 65 are 65, 13, 5, 1.
  • The common factors of 52 and 65 are 13, 1, intersecting the two sets above.
  • In the intersection factors of 52 ∩ factors of 65 the greatest element is 13.
  • Therefore, the greatest common factor of 52 and 65 is 13.

Taking the above into account you also know how to find all the common factors of 52 and 65, not just the greatest. In the next section we show you how to calculate the gcf of fifty-two and sixty-five by means of two more methods.

How to find the GCF of 52 and 65

The greatest common factor of 52 and 65 can be computed by using the least common multiple aka lcm of 52 and 65. This is the easiest approach:

gcf (52,65) = $\frac{52 \times 65}{lcm(52,65)} = \frac{3380}{260}$ = 13

Alternatively, the gcf of 52 and 65 can be found using the prime factorization of 52 and 65:

  • The prime factorization of 52 is: 2 x 2 x 13
  • The prime factorization of 65 is: 5 x 13
  • The prime factors and multiplicities 52 and 65 have in common are: 13
  • 13 is the gcf of 52 and 65
  • gcf(52,65) = 13

In any case, the easiest way to compute the gcf of two numbers like 52 and 65 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 52,65. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 52 and 65

What is the greatest common factor of 52 and 65 used for? Answer: It is helpful for reducing fractions like 52 / 65. Just divide the nominator as well as the denominator by the gcf (52,65) to reduce the fraction to lowest terms.

$\frac{52}{65} = \frac{\frac{52}{13}}{\frac{65}{13}} = \frac{4}{5}$.

Properties of GCF of 52 and 65

The most important properties of the gcf(52,65) are:

  • Commutative property: gcf(52,65) = gcf(65,52)
  • Associative property: gcf(52,65,n) = gcf(gcf(65,52),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

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 52 and 65 is 13. In common notation: gcf (52,65) = 13.

If you have been searching for gcf 52 and 65 or gcf 52 65 then you have come to the correct page, too. The same is the true if you typed gcf for 52 and 65 in your favorite search engine.

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

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