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...
Frequently searched terms on our site also include:

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.

Questions and comments related to the gcf of 34 and 51 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 34 and 51 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Posted in Greatest Common Factor

Leave a Reply

Your email address will not be published. Required fields are marked *

*


Related pages


factor tree of 81what are the prime factors of 125is 179 a prime numbergcf of 69 and 92is 197 a prime numbermultiplication chart 1-30prime factorization of 83prime factorization for 8greatest common factor of 35 and 63what is the factor tree of 63what is the gcf of 33 and 66prime factors of 84composite numbers 1 1000multiplication table up to 1000is 169 a prime numberwhat is the prime factorization of 750common multiples of 6 and 10what is the prime factorization of 175factor gcf calculatorwrite the prime factorization of 27common multiples of 2 3 4multiplication table 35x35prime factorization of 103write 88 as a product of prime factorsprime factor of 92what is 36 as a product of prime factorscommon multiples of 10greatest common factor of 28 and 70what is the prime factorization 56what are the prime factors of 125prime factorization 381-30 multiplication chartlcm of 120 and 150hcf of 60 and 75is 467 a prime numbercommon multiples of 5 and 9prime factorization 39is 18 a prime or composite numbermultiplication chart that goes to 100prime factorization of 82greatest common factor of 28 and 70is 147 a prime numbercommon multiples of 24 and 36 from 1 to 100what is the prime factorization of 825greatest common factor chartfind the prime factorization of 85prime factorization of 11555x tablesprime factorizations of 36is 199 a prime numberprime factorization of 5509times tablewhat is the prime factorization of 17499 prime factorization6x tables chartprime factorization of 750write 108 as a product of prime factorswhat is the prime factorization for 132what is the greatest common factor of 18 and 63is 24 a prime number or a composite numberis 221 a prime numbergcf of 54 and 63prime factorization 42prime factorization of 150what is the prime factorization of 847x tablesleast common multiples of 3 and 4common multiples of 6 and 756 as a product of prime factorsprime factorization of 294least common multiples chartwrite the prime factorization of 20what is the prime factorization of 84prime factors of 57express 56 as a product of its prime factorscommon multiples of 3 and 9easiest way to find greatest common factorwhat is the prime factorization of 333common multiples of 10multiplication table to 300prime factorization of 624