GCF of 66 and 33


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

What is the GCF of 66 and 33

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

gcf(66,33) = 33

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

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

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

How to find the GCF of 66 and 33

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

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

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

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

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

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

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

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

Properties of GCF of 66 and 33

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

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

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

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

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