GCF of 33 and 66


The gcf of 33 and 66 is the largest positive integer that divides the numbers 33 and 66 without a remainder. Spelled out, it is the greatest common factor of 33 and 66. Here you can find the gcf of 33 and 66, 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 33 and 66, but also that of three or more integers including thirty-three and sixty-six for example. Keep reading to learn everything about the gcf (33,66) and the terms related to it.

What is the GCF of 33 and 66

If you just want to know what is the greatest common factor of 33 and 66, it is 33. Usually, this is written as

gcf(33,66) = 33

The gcf of 33 and 66 can be obtained like this:

  • The factors of 33 are 33, 11, 3, 1.
  • The factors of 66 are 66, 33, 22, 11, 6, 3, 2, 1.
  • The common factors of 33 and 66 are 33, 11, 3, 1, intersecting the two sets above.
  • In the intersection factors of 33 ∩ factors of 66 the greatest element is 33.
  • Therefore, the greatest common factor of 33 and 66 is 33.

Taking the above into account you also know how to find all the common factors of 33 and 66, not just the greatest. In the next section we show you how to calculate the gcf of thirty-three and sixty-six by means of two more methods.

How to find the GCF of 33 and 66

The greatest common factor of 33 and 66 can be computed by using the least common multiple aka lcm of 33 and 66. This is the easiest approach:

gcf (33,66) = $\frac{33 \times 66}{lcm(33,66)} = \frac{2178}{66}$ = 33

Alternatively, the gcf of 33 and 66 can be found using the prime factorization of 33 and 66:

  • The prime factorization of 33 is: 3 x 11
  • The prime factorization of 66 is: 2 x 3 x 11
  • The prime factors and multiplicities 33 and 66 have in common are: 3 x 11
  • 3 x 11 is the gcf of 33 and 66
  • gcf(33,66) = 33

In any case, the easiest way to compute the gcf of two numbers like 33 and 66 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 33,66. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 33 and 66

What is the greatest common factor of 33 and 66 used for? Answer: It is helpful for reducing fractions like 33 / 66. Just divide the nominator as well as the denominator by the gcf (33,66) to reduce the fraction to lowest terms.

$\frac{33}{66} = \frac{\frac{33}{33}}{\frac{66}{33}} = \frac{1}{2}$.

Properties of GCF of 33 and 66

The most important properties of the gcf(33,66) are:

  • Commutative property: gcf(33,66) = gcf(66,33)
  • Associative property: gcf(33,66,n) = gcf(gcf(66,33),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 33 and 66 is 33. In common notation: gcf (33,66) = 33.

If you have been searching for gcf 33 and 66 or gcf 33 66 then you have come to the correct page, too. The same is the true if you typed gcf for 33 and 66 in your favorite search engine.

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

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