GCF of 39 and 52


The gcf of 39 and 52 is the largest positive integer that divides the numbers 39 and 52 without a remainder. Spelled out, it is the greatest common factor of 39 and 52. Here you can find the gcf of 39 and 52, 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 39 and 52, but also that of three or more integers including thirty-nine and fifty-two for example. Keep reading to learn everything about the gcf (39,52) and the terms related to it.

What is the GCF of 39 and 52

If you just want to know what is the greatest common factor of 39 and 52, it is 13. Usually, this is written as

gcf(39,52) = 13

The gcf of 39 and 52 can be obtained like this:

  • The factors of 39 are 39, 13, 3, 1.
  • The factors of 52 are 52, 26, 13, 4, 2, 1.
  • The common factors of 39 and 52 are 13, 1, intersecting the two sets above.
  • In the intersection factors of 39 ∩ factors of 52 the greatest element is 13.
  • Therefore, the greatest common factor of 39 and 52 is 13.

Taking the above into account you also know how to find all the common factors of 39 and 52, not just the greatest. In the next section we show you how to calculate the gcf of thirty-nine and fifty-two by means of two more methods.

How to find the GCF of 39 and 52

The greatest common factor of 39 and 52 can be computed by using the least common multiple aka lcm of 39 and 52. This is the easiest approach:

gcf (39,52) = $\frac{39 \times 52}{lcm(39,52)} = \frac{2028}{156}$ = 13

Alternatively, the gcf of 39 and 52 can be found using the prime factorization of 39 and 52:

  • The prime factorization of 39 is: 3 x 13
  • The prime factorization of 52 is: 2 x 2 x 13
  • The prime factors and multiplicities 39 and 52 have in common are: 13
  • 13 is the gcf of 39 and 52
  • gcf(39,52) = 13

In any case, the easiest way to compute the gcf of two numbers like 39 and 52 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 39,52. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 39 and 52

What is the greatest common factor of 39 and 52 used for? Answer: It is helpful for reducing fractions like 39 / 52. Just divide the nominator as well as the denominator by the gcf (39,52) to reduce the fraction to lowest terms.

$\frac{39}{52} = \frac{\frac{39}{13}}{\frac{52}{13}} = \frac{3}{4}$.

Properties of GCF of 39 and 52

The most important properties of the gcf(39,52) are:

  • Commutative property: gcf(39,52) = gcf(52,39)
  • Associative property: gcf(39,52,n) = gcf(gcf(52,39),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 39 and 52 is 13. In common notation: gcf (39,52) = 13.

If you have been searching for gcf 39 and 52 or gcf 39 52 then you have come to the correct page, too. The same is the true if you typed gcf for 39 and 52 in your favorite search engine.

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

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