GCF of 72 and 54


The gcf of 72 and 54 is the largest positive integer that divides the numbers 72 and 54 without a remainder. Spelled out, it is the greatest common factor of 72 and 54. Here you can find the gcf of 72 and 54, 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 72 and 54, but also that of three or more integers including seventy-two and fifty-four for example. Keep reading to learn everything about the gcf (72,54) and the terms related to it.

What is the GCF of 72 and 54

If you just want to know what is the greatest common factor of 72 and 54, it is 18. Usually, this is written as

gcf(72,54) = 18

The gcf of 72 and 54 can be obtained like this:

  • The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1.
  • The factors of 54 are 54, 27, 18, 9, 6, 3, 2, 1.
  • The common factors of 72 and 54 are 18, 9, 6, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 72 ∩ factors of 54 the greatest element is 18.
  • Therefore, the greatest common factor of 72 and 54 is 18.

Taking the above into account you also know how to find all the common factors of 72 and 54, not just the greatest. In the next section we show you how to calculate the gcf of seventy-two and fifty-four by means of two more methods.

How to find the GCF of 72 and 54

The greatest common factor of 72 and 54 can be computed by using the least common multiple aka lcm of 72 and 54. This is the easiest approach:

gcf (72,54) = $\frac{72 \times 54}{lcm(72,54)} = \frac{3888}{216}$ = 18

Alternatively, the gcf of 72 and 54 can be found using the prime factorization of 72 and 54:

  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • The prime factorization of 54 is: 2 x 3 x 3 x 3
  • The prime factors and multiplicities 72 and 54 have in common are: 2 x 3 x 3
  • 2 x 3 x 3 is the gcf of 72 and 54
  • gcf(72,54) = 18

In any case, the easiest way to compute the gcf of two numbers like 72 and 54 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 72,54. The calculation is conducted automatically.

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

Use of GCF of 72 and 54

What is the greatest common factor of 72 and 54 used for? Answer: It is helpful for reducing fractions like 72 / 54. Just divide the nominator as well as the denominator by the gcf (72,54) to reduce the fraction to lowest terms.

$\frac{72}{54} = \frac{\frac{72}{18}}{\frac{54}{18}} = \frac{4}{3}$.

Properties of GCF of 72 and 54

The most important properties of the gcf(72,54) are:

  • Commutative property: gcf(72,54) = gcf(54,72)
  • Associative property: gcf(72,54,n) = gcf(gcf(54,72),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 72 and 54 is 18. In common notation: gcf (72,54) = 18.

If you have been searching for gcf 72 and 54 or gcf 72 54 then you have come to the correct page, too. The same is the true if you typed gcf for 72 and 54 in your favorite search engine.

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

Questions and comments related to the gcf of 72 and 54 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 72 and 54 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


greatest prime factor of 68what is the prime factorization of 138is 72 a prime or composite numberfactorization of 180which of the factors of 100 are prime numberswhat is the lcm of 5 and 10lcm of 144what is the prime factorization of 43prime factorization of 152time table chart 1-100greatest common factor of 34 and 51common multiples of 10the prime factorization of 12056 as a product of prime factorsprime factorization for 300whats a prime factorcommon denominator of 5 and 10prime factorization for 56prime factors of 300is 107 a composite numberfind the prime factorization of 16512x tablesthe prime factorization of 180what are the prime factors of 62520 by 20 multiplication chartprime factorization of 735what is the prime factors of 81prime factors of 462what is the prime factorization of 71prime factorization of 156common multiples of 5 and 7what is the prime factorization of 133100-84write the prime factorization of 20printable multiplication table 1-20common multiples of 3 and 6the prime factorization of 75prime factorization of 294prime factorization for 300greatest common factor of 45 and 721-100 multiplication tableprime factorization 51common denominator of 7 and 12prime factorization of 130the prime factorization of 68the prime factorization of 52greatest common factor of 35 and 36prime factorization for 55write 18 as a product of prime factorswhat is the greatest common factor of 42 and 72what is the prime factorization for 38gcf of 144prime factorization of 6720 by 20 multiplication chartprime factorization of 87greatest common factor of 54 and 36prime factors of 293prime factor of 76is 125 a prime or composite numbermultiplication table 1-50common multiples of 6 and 15what is the greatest common factor of 63 and 81gcf and lcm finderprime factorization of 111is 997 a prime numbermultiplication table 1-10034-24-34times table 20x20the prime factorization of 175the prime factorization of 104highest common factor of 72 and 96the prime factorization of 180multiplication chart 40x40find the prime factorization of 42what are the prime factors of 64what is the prime factorization of 39printable multiplication table 1-100