GCF of 10 and 17


The gcf of 10 and 17 is the largest positive integer that divides the numbers 10 and 17 without a remainder. Spelled out, it is the greatest common factor of 10 and 17. Here you can find the gcf of 10 and 17, 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 10 and 17, but also that of three or more integers including ten and seventeen for example. Keep reading to learn everything about the gcf (10,17) and the terms related to it.

What is the GCF of 10 and 17

If you just want to know what is the greatest common factor of 10 and 17, it is 1. Usually, this is written as

gcf(10,17) = 1

The gcf of 10 and 17 can be obtained like this:

  • The factors of 10 are 10, 5, 2, 1.
  • The factors of 17 are 17, 1.
  • The common factors of 10 and 17 are 1, intersecting the two sets above.
  • In the intersection factors of 10 ∩ factors of 17 the greatest element is 1.
  • Therefore, the greatest common factor of 10 and 17 is 1.

Taking the above into account you also know how to find all the common factors of 10 and 17, not just the greatest. In the next section we show you how to calculate the gcf of ten and seventeen by means of two more methods.

How to find the GCF of 10 and 17

The greatest common factor of 10 and 17 can be computed by using the least common multiple aka lcm of 10 and 17. This is the easiest approach:

gcf (10,17) = $\frac{10 \times 17}{lcm(10,17)} = \frac{170}{170}$ = 1

Alternatively, the gcf of 10 and 17 can be found using the prime factorization of 10 and 17:

  • The prime factorization of 10 is: 2 x 5
  • The prime factorization of 17 is: 17
  • The prime factors and multiplicities 10 and 17 have in common are: 1
  • 1 is the gcf of 10 and 17
  • gcf(10,17) = 1

In any case, the easiest way to compute the gcf of two numbers like 10 and 17 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 10,17. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 10 and 17

What is the greatest common factor of 10 and 17 used for? Answer: It is helpful for reducing fractions like 10 / 17. Just divide the nominator as well as the denominator by the gcf (10,17) to reduce the fraction to lowest terms.

$\frac{10}{17} = \frac{\frac{10}{1}}{\frac{17}{1}} = \frac{10}{17}$.

Properties of GCF of 10 and 17

The most important properties of the gcf(10,17) are:

  • Commutative property: gcf(10,17) = gcf(17,10)
  • Associative property: gcf(10,17,n) = gcf(gcf(17,10),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 10 and 17 is 1. In common notation: gcf (10,17) = 1.

If you have been searching for gcf 10 and 17 or gcf 10 17 then you have come to the correct page, too. The same is the true if you typed gcf for 10 and 17 in your favorite search engine.

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

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