GCF of 12 and 30


The gcf of 12 and 30 is the largest positive integer that divides the numbers 12 and 30 without a remainder. Spelled out, it is the greatest common factor of 12 and 30. Here you can find the gcf of 12 and 30, 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 12 and 30, but also that of three or more integers including twelve and thirty for example. Keep reading to learn everything about the gcf (12,30) and the terms related to it.

What is the GCF of 12 and 30

If you just want to know what is the greatest common factor of 12 and 30, it is 6. Usually, this is written as

gcf(12,30) = 6

The gcf of 12 and 30 can be obtained like this:

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

Taking the above into account you also know how to find all the common factors of 12 and 30, not just the greatest. In the next section we show you how to calculate the gcf of twelve and thirty by means of two more methods.

How to find the GCF of 12 and 30

The greatest common factor of 12 and 30 can be computed by using the least common multiple aka lcm of 12 and 30. This is the easiest approach:

gcf (12,30) = $\frac{12 \times 30}{lcm(12,30)} = \frac{360}{60}$ = 6

Alternatively, the gcf of 12 and 30 can be found using the prime factorization of 12 and 30:

  • The prime factorization of 12 is: 2 x 2 x 3
  • The prime factorization of 30 is: 2 x 3 x 5
  • The prime factors and multiplicities 12 and 30 have in common are: 2 x 3
  • 2 x 3 is the gcf of 12 and 30
  • gcf(12,30) = 6

In any case, the easiest way to compute the gcf of two numbers like 12 and 30 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 12,30. The calculation is conducted automatically.

The gcf is...
Frequently searched terms on our site also include:

Use of GCF of 12 and 30

What is the greatest common factor of 12 and 30 used for? Answer: It is helpful for reducing fractions like 12 / 30. Just divide the nominator as well as the denominator by the gcf (12,30) to reduce the fraction to lowest terms.

$\frac{12}{30} = \frac{\frac{12}{6}}{\frac{30}{6}} = \frac{2}{5}$.

Properties of GCF of 12 and 30

The most important properties of the gcf(12,30) are:

  • Commutative property: gcf(12,30) = gcf(30,12)
  • Associative property: gcf(12,30,n) = gcf(gcf(30,12),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 12 and 30 is 6. In common notation: gcf (12,30) = 6.

If you have been searching for gcf 12 and 30 or gcf 12 30 then you have come to the correct page, too. The same is the true if you typed gcf for 12 and 30 in your favorite search engine.

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

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