Home » Greatest Common Factor » GCF of 82 and 3

GCF of 82 and 3

  • by

The gcf of 82 and 3 is the largest positive integer that divides the numbers 82 and 3 without a remainder. Spelled out, it is the greatest common factor of 82 and 3. Here you can find the gcf of 82 and 3, 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 82 and 3, but also that of three or more integers including eighty-two and three for example. Keep reading to learn everything about the gcf (82,3) and the terms related to it.

What is the GCF of 82 and 3

If you just want to know what is the greatest common factor of 82 and 3, it is 1. Usually, this is written as

gcf(82,3) = 1

The gcf of 82 and 3 can be obtained like this:

  • The factors of 82 are 82, 41, 2, 1.
  • The factors of 3 are 3, 1.
  • The common factors of 82 and 3 are 1, intersecting the two sets above.
  • In the intersection factors of 82 ∩ factors of 3 the greatest element is 1.
  • Therefore, the greatest common factor of 82 and 3 is 1.

Taking the above into account you also know how to find all the common factors of 82 and 3, not just the greatest. In the next section we show you how to calculate the gcf of eighty-two and three by means of two more methods.

How to find the GCF of 82 and 3

The greatest common factor of 82 and 3 can be computed by using the least common multiple aka lcm of 82 and 3. This is the easiest approach:

gcf (82,3) = \frac{82 \times 3}{lcm(82,3)} = \frac{246}{246} = 1

Alternatively, the gcf of 82 and 3 can be found using the prime factorization of 82 and 3:

  • The prime factorization of 82 is: 2 x 41
  • The prime factorization of 3 is: 3
  • The prime factors and multiplicities 82 and 3 have in common are: 1
  • 1 is the gcf of 82 and 3
  • gcf(82,3) = 1

In any case, the easiest way to compute the gcf of two numbers like 82 and 3 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 82,3. The calculation is conducted automatically.

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

Use of GCF of 82 and 3

What is the greatest common factor of 82 and 3 used for? Answer: It is helpful for reducing fractions like 82 / 3. Just divide the nominator as well as the denominator by the gcf (82,3) to reduce the fraction to lowest terms.

\frac{82}{3} = \frac{\frac{82}{1}}{\frac{3}{1}} = \frac{82}{3}.

Properties of GCF of 82 and 3

The most important properties of the gcf(82,3) are:

  • Commutative property: gcf(82,3) = gcf(3,82)
  • Associative property: gcf(82,3,n) = gcf(gcf(3,82),n) n\neq 0 \thinspace\in\thinspace\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 82 and 3 is 1. In common notation: gcf (82,3) = 1.

If you have been searching for gcf 82 and 3 or gcf 82 3 then you have come to the correct page, too. The same is the true if you typed gcf for 82 and 3 in your favorite search engine.

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

Questions and comments related to the gcf of 82 and 3 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 82 and 3 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email