GCF of 75 and 60


The gcf of 75 and 60 is the largest positive integer that divides the numbers 75 and 60 without a remainder. Spelled out, it is the greatest common factor of 75 and 60. Here you can find the gcf of 75 and 60, 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 75 and 60, but also that of three or more integers including seventy-five and sixty for example. Keep reading to learn everything about the gcf (75,60) and the terms related to it.

What is the GCF of 75 and 60

If you just want to know what is the greatest common factor of 75 and 60, it is 15. Usually, this is written as

gcf(75,60) = 15

The gcf of 75 and 60 can be obtained like this:

  • The factors of 75 are 75, 25, 15, 5, 3, 1.
  • The factors of 60 are 60, 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1.
  • The common factors of 75 and 60 are 15, 5, 3, 1, intersecting the two sets above.
  • In the intersection factors of 75 ∩ factors of 60 the greatest element is 15.
  • Therefore, the greatest common factor of 75 and 60 is 15.

Taking the above into account you also know how to find all the common factors of 75 and 60, not just the greatest. In the next section we show you how to calculate the gcf of seventy-five and sixty by means of two more methods.

How to find the GCF of 75 and 60

The greatest common factor of 75 and 60 can be computed by using the least common multiple aka lcm of 75 and 60. This is the easiest approach:

gcf (75,60) = $\frac{75 \times 60}{lcm(75,60)} = \frac{4500}{300}$ = 15

Alternatively, the gcf of 75 and 60 can be found using the prime factorization of 75 and 60:

  • The prime factorization of 75 is: 3 x 5 x 5
  • The prime factorization of 60 is: 2 x 2 x 3 x 5
  • The prime factors and multiplicities 75 and 60 have in common are: 3 x 5
  • 3 x 5 is the gcf of 75 and 60
  • gcf(75,60) = 15

In any case, the easiest way to compute the gcf of two numbers like 75 and 60 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 75,60. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 75 and 60

What is the greatest common factor of 75 and 60 used for? Answer: It is helpful for reducing fractions like 75 / 60. Just divide the nominator as well as the denominator by the gcf (75,60) to reduce the fraction to lowest terms.

$\frac{75}{60} = \frac{\frac{75}{15}}{\frac{60}{15}} = \frac{5}{4}$.

Properties of GCF of 75 and 60

The most important properties of the gcf(75,60) are:

  • Commutative property: gcf(75,60) = gcf(60,75)
  • Associative property: gcf(75,60,n) = gcf(gcf(60,75),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 75 and 60 is 15. In common notation: gcf (75,60) = 15.

If you have been searching for gcf 75 and 60 or gcf 75 60 then you have come to the correct page, too. The same is the true if you typed gcf for 75 and 60 in your favorite search engine.

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

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