GCF of 6 and 12


The gcf of 6 and 12 is the largest positive integer that divides the numbers 6 and 12 without a remainder. Spelled out, it is the greatest common factor of 6 and 12. Here you can find the gcf of 6 and 12, 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 12, but also that of three or more integers including six and twelve for example. Keep reading to learn everything about the gcf (6,12) and the terms related to it.

What is the GCF of 6 and 12

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

gcf(6,12) = 6

The gcf of 6 and 12 can be obtained like this:

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

Taking the above into account you also know how to find all the common factors of 6 and 12, not just the greatest. In the next section we show you how to calculate the gcf of six and twelve by means of two more methods.

How to find the GCF of 6 and 12

The greatest common factor of 6 and 12 can be computed by using the least common multiple aka lcm of 6 and 12. This is the easiest approach:

gcf (6,12) = $\frac{6 \times 12}{lcm(6,12)} = \frac{72}{12}$ = 6

Alternatively, the gcf of 6 and 12 can be found using the prime factorization of 6 and 12:

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

In any case, the easiest way to compute the gcf of two numbers like 6 and 12 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 6,12. The calculation is conducted automatically.

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

Use of GCF of 6 and 12

What is the greatest common factor of 6 and 12 used for? Answer: It is helpful for reducing fractions like 6 / 12. Just divide the nominator as well as the denominator by the gcf (6,12) to reduce the fraction to lowest terms.

$\frac{6}{12} = \frac{\frac{6}{6}}{\frac{12}{6}} = \frac{1}{2}$.

Properties of GCF of 6 and 12

The most important properties of the gcf(6,12) are:

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

If you have been searching for gcf 6 and 12 or gcf 6 12 then you have come to the correct page, too. The same is the true if you typed gcf for 6 and 12 in your favorite search engine.

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

Questions and comments related to the gcf of 6 and 12 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 6 and 12 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Posted in Greatest Common Factor

Leave a Reply

Your email address will not be published. Required fields are marked *

*


Related pages


prime factorization 252times tables 4xprime factors of 52is 57 a prime or composite numberprime factorization of 192find the greatest common factor of 270 and 360gcf calculaterwhat is the prime factorization of 210prime factorization of 500what is the lcm of 15gcf of 52 and 65multiplication chart 1-40prime factorization of 85is 143 a prime numberprime factor of 180greatest common factor of 42 and 63find the prime factorization of 90gcf calculatergcf of 28 and 98prime factor of 57prime factorization of 231prime factorization 441prime factorization 84write 600 as a product of its prime factorsthe prime factorization of 14464 prime factorizationmultiplication table printable 20x20find the greatest common factor of 270 and 360prime factorization for 104143 prime numberwhat is the greatest common factor of 56 and 64find the prime factorization of 63prime factorization of 72838-24-38prime factorization for 105196 prime factorizationfinding the gcf calculatorwrite 66 as a product of prime factors20 by 20 multiplication chartcommon multiples of 6 and 12prime factors of 210prime factorization of 750greatest common factor of 42 and 56what is the prime factorization of 2800what is the prime factorization of 153what are the prime factors of 132multiplication table 25x25 printableprime factorization 92what is the prime factorization for 38prime factorization of 350find the prime factorization of 84find the prime factorization of 78what is the lcm of 3 and 10least common multiples of 8 and 12prime factors of 250prime factor of 196what is the prime factorization of 464x times tableswhat is the greatest common factor of 60 and 72gcf of 90 and 108prime factorization of 147what is the greatest common factor of 72 and 54prime factorization of 147prime factorization 240prime factorization for 300multiplication table up to 200common multiples of 6 and 12common multiples of 5 and 936 multiplication factsgcf of 70 and 98prime factorization of 65what is prime factorization of 70