GCF of 56 and 72


The gcf of 56 and 72 is the largest positive integer that divides the numbers 56 and 72 without a remainder. Spelled out, it is the greatest common factor of 56 and 72. Here you can find the gcf of 56 and 72, 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 56 and 72, but also that of three or more integers including fifty-six and seventy-two for example. Keep reading to learn everything about the gcf (56,72) and the terms related to it.

What is the GCF of 56 and 72

If you just want to know what is the greatest common factor of 56 and 72, it is 8. Usually, this is written as

gcf(56,72) = 8

The gcf of 56 and 72 can be obtained like this:

  • The factors of 56 are 56, 28, 14, 8, 7, 4, 2, 1.
  • The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1.
  • The common factors of 56 and 72 are 8, 4, 2, 1, intersecting the two sets above.
  • In the intersection factors of 56 ∩ factors of 72 the greatest element is 8.
  • Therefore, the greatest common factor of 56 and 72 is 8.

Taking the above into account you also know how to find all the common factors of 56 and 72, not just the greatest. In the next section we show you how to calculate the gcf of fifty-six and seventy-two by means of two more methods.

How to find the GCF of 56 and 72

The greatest common factor of 56 and 72 can be computed by using the least common multiple aka lcm of 56 and 72. This is the easiest approach:

gcf (56,72) = $\frac{56 \times 72}{lcm(56,72)} = \frac{4032}{504}$ = 8

Alternatively, the gcf of 56 and 72 can be found using the prime factorization of 56 and 72:

  • The prime factorization of 56 is: 2 x 2 x 2 x 7
  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • The prime factors and multiplicities 56 and 72 have in common are: 2 x 2 x 2
  • 2 x 2 x 2 is the gcf of 56 and 72
  • gcf(56,72) = 8

In any case, the easiest way to compute the gcf of two numbers like 56 and 72 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 56,72. The calculation is conducted automatically.

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

Use of GCF of 56 and 72

What is the greatest common factor of 56 and 72 used for? Answer: It is helpful for reducing fractions like 56 / 72. Just divide the nominator as well as the denominator by the gcf (56,72) to reduce the fraction to lowest terms.

$\frac{56}{72} = \frac{\frac{56}{8}}{\frac{72}{8}} = \frac{7}{9}$.

Properties of GCF of 56 and 72

The most important properties of the gcf(56,72) are:

  • Commutative property: gcf(56,72) = gcf(72,56)
  • Associative property: gcf(56,72,n) = gcf(gcf(72,56),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 56 and 72 is 8. In common notation: gcf (56,72) = 8.

If you have been searching for gcf 56 and 72 or gcf 56 72 then you have come to the correct page, too. The same is the true if you typed gcf for 56 and 72 in your favorite search engine.

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

Questions and comments related to the gcf of 56 and 72 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 56 and 72 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


what is the largest prime factor of 200lcm of 5 7prime factorization of 440common multiples of 4 and 11what is the prime factorization of 72prime factorization for 144prime factorization of 63what is the lcm of 12is 14 a prime or composite numbergcf of 3multiplication table 30x30find the prime factorization of 140what is the gcf of 35 and 63what is the gcf of 33 and 66prime factorization of 380is 211 a prime numbertimes table 25x25prime factorization of 148prime factor tree of 81gcf of 75 and 60what are the prime factors of 66100-72prime factorization 110common multiples of 3 and 15gcf of 17 and 85find the prime factorization of 105greatest factor calculatorcommon multiples of 6common multiples of 10largest common denominator calculator56 as a product of prime factorsprime factorization of 103prime factorization of 39prime factors of 74gcf of 70 and 98what is the prime factorization of 344gcf of 40 and 64write 88 as a product of prime factorsprime factorization for 64times table chart 1 1000common multiples of 6 and 15common multiples of 8what is the prime factorization of 140prime factorization of 95prime factorization of 164is 27 a prime number or compositemultiplication table 1-30find the prime factorization of 125what is the lcm of 4 and 10gcf and lcm of 36 and 45gcf monomial calculatorwhat is the greatest common factor of 96 and 64prime factorization 343greatest prime factor of 100prime factorization 39common multiples of 6 and 15write 42 as a product of prime factorsprime factorization of 365factor tree of 77whats a prime factordefine lowest common multiplenineandsixteen100-841 to 100 multiplication tablewhat is the greatest common factor of 63 and 81hcf of 60 and 75147 prime numberprime factorization of 104common multiples of 6 and 10prime factorization 13560 multiplication tablegcf of 48 and 64prime factorization of 189prime factorization for 66find the prime factorization of 28lowest common multiple of 60 and 96what is prime factorization of 70prime factorization of 462prime factorization of 240