GCF of 34 and 51


The gcf of 34 and 51 is the largest positive integer that divides the numbers 34 and 51 without a remainder. Spelled out, it is the greatest common factor of 34 and 51. Here you can find the gcf of 34 and 51, 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 34 and 51, but also that of three or more integers including thirty-four and fifty-one for example. Keep reading to learn everything about the gcf (34,51) and the terms related to it.

What is the GCF of 34 and 51

If you just want to know what is the greatest common factor of 34 and 51, it is 17. Usually, this is written as

gcf(34,51) = 17

The gcf of 34 and 51 can be obtained like this:

  • The factors of 34 are 34, 17, 2, 1.
  • The factors of 51 are 51, 17, 3, 1.
  • The common factors of 34 and 51 are 17, 1, intersecting the two sets above.
  • In the intersection factors of 34 ∩ factors of 51 the greatest element is 17.
  • Therefore, the greatest common factor of 34 and 51 is 17.

Taking the above into account you also know how to find all the common factors of 34 and 51, not just the greatest. In the next section we show you how to calculate the gcf of thirty-four and fifty-one by means of two more methods.

How to find the GCF of 34 and 51

The greatest common factor of 34 and 51 can be computed by using the least common multiple aka lcm of 34 and 51. This is the easiest approach:

gcf (34,51) = $\frac{34 \times 51}{lcm(34,51)} = \frac{1734}{102}$ = 17

Alternatively, the gcf of 34 and 51 can be found using the prime factorization of 34 and 51:

  • The prime factorization of 34 is: 2 x 17
  • The prime factorization of 51 is: 3 x 17
  • The prime factors and multiplicities 34 and 51 have in common are: 17
  • 17 is the gcf of 34 and 51
  • gcf(34,51) = 17

In any case, the easiest way to compute the gcf of two numbers like 34 and 51 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 34,51. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 34 and 51

What is the greatest common factor of 34 and 51 used for? Answer: It is helpful for reducing fractions like 34 / 51. Just divide the nominator as well as the denominator by the gcf (34,51) to reduce the fraction to lowest terms.

$\frac{34}{51} = \frac{\frac{34}{17}}{\frac{51}{17}} = \frac{2}{3}$.

Properties of GCF of 34 and 51

The most important properties of the gcf(34,51) are:

  • Commutative property: gcf(34,51) = gcf(51,34)
  • Associative property: gcf(34,51,n) = gcf(gcf(51,34),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 34 and 51 is 17. In common notation: gcf (34,51) = 17.

If you have been searching for gcf 34 and 51 or gcf 34 51 then you have come to the correct page, too. The same is the true if you typed gcf for 34 and 51 in your favorite search engine.

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

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