GCF of 5 and 10


The gcf of 5 and 10 is the largest positive integer that divides the numbers 5 and 10 without a remainder. Spelled out, it is the greatest common factor of 5 and 10. Here you can find the gcf of 5 and 10, 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 5 and 10, but also that of three or more integers including five and ten for example. Keep reading to learn everything about the gcf (5,10) and the terms related to it.

What is the GCF of 5 and 10

If you just want to know what is the greatest common factor of 5 and 10, it is 5. Usually, this is written as

gcf(5,10) = 5

The gcf of 5 and 10 can be obtained like this:

  • The factors of 5 are 5, 1.
  • The factors of 10 are 10, 5, 2, 1.
  • The common factors of 5 and 10 are 5, 1, intersecting the two sets above.
  • In the intersection factors of 5 ∩ factors of 10 the greatest element is 5.
  • Therefore, the greatest common factor of 5 and 10 is 5.

Taking the above into account you also know how to find all the common factors of 5 and 10, not just the greatest. In the next section we show you how to calculate the gcf of five and ten by means of two more methods.

How to find the GCF of 5 and 10

The greatest common factor of 5 and 10 can be computed by using the least common multiple aka lcm of 5 and 10. This is the easiest approach:

gcf (5,10) = $\frac{5 \times 10}{lcm(5,10)} = \frac{50}{10}$ = 5

Alternatively, the gcf of 5 and 10 can be found using the prime factorization of 5 and 10:

  • The prime factorization of 5 is: 5
  • The prime factorization of 10 is: 2 x 5
  • The prime factors and multiplicities 5 and 10 have in common are: 5
  • 5 is the gcf of 5 and 10
  • gcf(5,10) = 5

In any case, the easiest way to compute the gcf of two numbers like 5 and 10 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 5,10. The calculation is conducted automatically.

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

Use of GCF of 5 and 10

What is the greatest common factor of 5 and 10 used for? Answer: It is helpful for reducing fractions like 5 / 10. Just divide the nominator as well as the denominator by the gcf (5,10) to reduce the fraction to lowest terms.

$\frac{5}{10} = \frac{\frac{5}{5}}{\frac{10}{5}} = \frac{1}{2}$.

Properties of GCF of 5 and 10

The most important properties of the gcf(5,10) are:

  • Commutative property: gcf(5,10) = gcf(10,5)
  • Associative property: gcf(5,10,n) = gcf(gcf(10,5),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 5 and 10 is 5. In common notation: gcf (5,10) = 5.

If you have been searching for gcf 5 and 10 or gcf 5 10 then you have come to the correct page, too. The same is the true if you typed gcf for 5 and 10 in your favorite search engine.

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

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