GCF of 3 and 9


The gcf of 3 and 9 is the largest positive integer that divides the numbers 3 and 9 without a remainder. Spelled out, it is the greatest common factor of 3 and 9. Here you can find the gcf of 3 and 9, 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 3 and 9, but also that of three or more integers including three and nine for example. Keep reading to learn everything about the gcf (3,9) and the terms related to it.

What is the GCF of 3 and 9

If you just want to know what is the greatest common factor of 3 and 9, it is 3. Usually, this is written as

gcf(3,9) = 3

The gcf of 3 and 9 can be obtained like this:

  • The factors of 3 are 3, 1.
  • The factors of 9 are 9, 3, 1.
  • The common factors of 3 and 9 are 3, 1, intersecting the two sets above.
  • In the intersection factors of 3 ∩ factors of 9 the greatest element is 3.
  • Therefore, the greatest common factor of 3 and 9 is 3.

Taking the above into account you also know how to find all the common factors of 3 and 9, not just the greatest. In the next section we show you how to calculate the gcf of three and nine by means of two more methods.

How to find the GCF of 3 and 9

The greatest common factor of 3 and 9 can be computed by using the least common multiple aka lcm of 3 and 9. This is the easiest approach:

gcf (3,9) = $\frac{3 \times 9}{lcm(3,9)} = \frac{27}{9}$ = 3

Alternatively, the gcf of 3 and 9 can be found using the prime factorization of 3 and 9:

  • The prime factorization of 3 is: 3
  • The prime factorization of 9 is: 3 x 3
  • The prime factors and multiplicities 3 and 9 have in common are: 3
  • 3 is the gcf of 3 and 9
  • gcf(3,9) = 3

In any case, the easiest way to compute the gcf of two numbers like 3 and 9 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 3,9. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 3 and 9

What is the greatest common factor of 3 and 9 used for? Answer: It is helpful for reducing fractions like 3 / 9. Just divide the nominator as well as the denominator by the gcf (3,9) to reduce the fraction to lowest terms.

$\frac{3}{9} = \frac{\frac{3}{3}}{\frac{9}{3}} = \frac{1}{3}$.

Properties of GCF of 3 and 9

The most important properties of the gcf(3,9) are:

  • Commutative property: gcf(3,9) = gcf(9,3)
  • Associative property: gcf(3,9,n) = gcf(gcf(9,3),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 3 and 9 is 3. In common notation: gcf (3,9) = 3.

If you have been searching for gcf 3 and 9 or gcf 3 9 then you have come to the correct page, too. The same is the true if you typed gcf for 3 and 9 in your favorite search engine.

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

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