GCF of 6 and 48


The gcf of 6 and 48 is the largest positive integer that divides the numbers 6 and 48 without a remainder. Spelled out, it is the greatest common factor of 6 and 48. Here you can find the gcf of 6 and 48, 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 6 and 48, but also that of three or more integers including six and forty-eight for example. Keep reading to learn everything about the gcf (6,48) and the terms related to it.

What is the GCF of 6 and 48

If you just want to know what is the greatest common factor of 6 and 48, it is 6. Usually, this is written as

gcf(6,48) = 6

The gcf of 6 and 48 can be obtained like this:

  • The factors of 6 are 6, 3, 2, 1.
  • The factors of 48 are 48, 24, 16, 12, 8, 6, 4, 3, 2, 1.
  • The common factors of 6 and 48 are 6, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 6 ∩ factors of 48 the greatest element is 6.
  • Therefore, the greatest common factor of 6 and 48 is 6.

Taking the above into account you also know how to find all the common factors of 6 and 48, not just the greatest. In the next section we show you how to calculate the gcf of six and forty-eight by means of two more methods.

How to find the GCF of 6 and 48

The greatest common factor of 6 and 48 can be computed by using the least common multiple aka lcm of 6 and 48. This is the easiest approach:

gcf (6,48) = $\frac{6 \times 48}{lcm(6,48)} = \frac{288}{48}$ = 6

Alternatively, the gcf of 6 and 48 can be found using the prime factorization of 6 and 48:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 48 is: 2 x 2 x 2 x 2 x 3
  • The prime factors and multiplicities 6 and 48 have in common are: 2 x 3
  • 2 x 3 is the gcf of 6 and 48
  • gcf(6,48) = 6

In any case, the easiest way to compute the gcf of two numbers like 6 and 48 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 6,48. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 6 and 48

What is the greatest common factor of 6 and 48 used for? Answer: It is helpful for reducing fractions like 6 / 48. Just divide the nominator as well as the denominator by the gcf (6,48) to reduce the fraction to lowest terms.

$\frac{6}{48} = \frac{\frac{6}{6}}{\frac{48}{6}} = \frac{1}{8}$.

Properties of GCF of 6 and 48

The most important properties of the gcf(6,48) are:

  • Commutative property: gcf(6,48) = gcf(48,6)
  • Associative property: gcf(6,48,n) = gcf(gcf(48,6),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 6 and 48 is 6. In common notation: gcf (6,48) = 6.

If you have been searching for gcf 6 and 48 or gcf 6 48 then you have come to the correct page, too. The same is the true if you typed gcf for 6 and 48 in your favorite search engine.

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

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