GCF of 64 and 56


The gcf of 64 and 56 is the largest positive integer that divides the numbers 64 and 56 without a remainder. Spelled out, it is the greatest common factor of 64 and 56. Here you can find the gcf of 64 and 56, 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 64 and 56, but also that of three or more integers including sixty-four and fifty-six for example. Keep reading to learn everything about the gcf (64,56) and the terms related to it.

What is the GCF of 64 and 56

If you just want to know what is the greatest common factor of 64 and 56, it is 8. Usually, this is written as

gcf(64,56) = 8

The gcf of 64 and 56 can be obtained like this:

  • The factors of 64 are 64, 32, 16, 8, 4, 2, 1.
  • The factors of 56 are 56, 28, 14, 8, 7, 4, 2, 1.
  • The common factors of 64 and 56 are 8, 4, 2, 1, intersecting the two sets above.
  • In the intersection factors of 64 ∩ factors of 56 the greatest element is 8.
  • Therefore, the greatest common factor of 64 and 56 is 8.

Taking the above into account you also know how to find all the common factors of 64 and 56, not just the greatest. In the next section we show you how to calculate the gcf of sixty-four and fifty-six by means of two more methods.

How to find the GCF of 64 and 56

The greatest common factor of 64 and 56 can be computed by using the least common multiple aka lcm of 64 and 56. This is the easiest approach:

gcf (64,56) = $\frac{64 \times 56}{lcm(64,56)} = \frac{3584}{448}$ = 8

Alternatively, the gcf of 64 and 56 can be found using the prime factorization of 64 and 56:

  • The prime factorization of 64 is: 2 x 2 x 2 x 2 x 2 x 2
  • The prime factorization of 56 is: 2 x 2 x 2 x 7
  • The prime factors and multiplicities 64 and 56 have in common are: 2 x 2 x 2
  • 2 x 2 x 2 is the gcf of 64 and 56
  • gcf(64,56) = 8

In any case, the easiest way to compute the gcf of two numbers like 64 and 56 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 64,56. The calculation is conducted automatically.

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

Use of GCF of 64 and 56

What is the greatest common factor of 64 and 56 used for? Answer: It is helpful for reducing fractions like 64 / 56. Just divide the nominator as well as the denominator by the gcf (64,56) to reduce the fraction to lowest terms.

$\frac{64}{56} = \frac{\frac{64}{8}}{\frac{56}{8}} = \frac{8}{7}$.

Properties of GCF of 64 and 56

The most important properties of the gcf(64,56) are:

  • Commutative property: gcf(64,56) = gcf(56,64)
  • Associative property: gcf(64,56,n) = gcf(gcf(56,64),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 64 and 56 is 8. In common notation: gcf (64,56) = 8.

If you have been searching for gcf 64 and 56 or gcf 64 56 then you have come to the correct page, too. The same is the true if you typed gcf for 64 and 56 in your favorite search engine.

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

Questions and comments related to the gcf of 64 and 56 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 64 and 56 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


prime factorization 132what is the prime factorization of 210what is the gcf of 96 and 84greatest common factor of 64 and 48what is the gcf of 63what is the greatest common factor of 54 and 63gcf of 90 and 75gcf of 65what are the prime factors of 385common multiples of 3 and 7printable multiplication table 1-100lowest common multiple of 60 and 96multiplication chart to 500prime factorization for 9897 prime factorizationprime factorization for 9020x multiplication tablecommon multiples of 16 and 18prime factorization 63find the prime factorization of 75common denominator of 5 and 8find the prime factorization of 175prime factorization of 308what is the prime factorization of 133greatest common factor of 72 and 108multiplication table 1-30what is the prime factors of 90multiplication tables upto 20 pdfwhat is the greatest common factor of 72 and 81prime factorization of 245what are the divisors of 64prime factorization for 46what is the prime factorization for 150multiplication 30x30gcf of 49 and 81common multiples of 2 and 6gcf of 75 and 60196 prime factorization8x tablescommon multiples of 6 and 7whats the prime factorization of 50prime factorization of 67prime factorization for 216prime factorization of 49prime factorization of 70prime factorization for 5536 multiplication factsprime factor of 51factorization of 196greatest common factor of 48 and 64what is the prime factorization of 221gcf of 96 and 144what are the prime factors of 125what is the prime factorization for 150what is the lcm of 3 5100-78what are the common multiples of 2 and 3prime factorization of 55table of multiplication 1-100prime numbers 1-500factor gcf calculatorwhat is the greatest common factor of 36 and 5444 as a product of prime factorsprime factor of 91prime factorization of 429determine the prime factorization of 90what is the lcm of 4 and 61-20 multiplication chartwhat are the prime factors of 751-100 multiplication tablewhat is the greatest common factor of 42 and 63sevens times tablesprime factorization of 735what is the prime factorization of 6620 by 20 multiplication chartprime factorization of 123common multiples of 6 and 7what is the gcf of 84 and 96