GCF of 24 and 84


The gcf of 24 and 84 is the largest positive integer that divides the numbers 24 and 84 without a remainder. Spelled out, it is the greatest common factor of 24 and 84. Here you can find the gcf of 24 and 84, 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 24 and 84, but also that of three or more integers including twenty-four and eighty-four for example. Keep reading to learn everything about the gcf (24,84) and the terms related to it.

What is the GCF of 24 and 84

If you just want to know what is the greatest common factor of 24 and 84, it is 12. Usually, this is written as

gcf(24,84) = 12

The gcf of 24 and 84 can be obtained like this:

  • The factors of 24 are 24, 12, 8, 6, 4, 3, 2, 1.
  • The factors of 84 are 84, 42, 28, 21, 14, 12, 7, 6, 4, 3, 2, 1.
  • The common factors of 24 and 84 are 12, 6, 4, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 24 ∩ factors of 84 the greatest element is 12.
  • Therefore, the greatest common factor of 24 and 84 is 12.

Taking the above into account you also know how to find all the common factors of 24 and 84, not just the greatest. In the next section we show you how to calculate the gcf of twenty-four and eighty-four by means of two more methods.

How to find the GCF of 24 and 84

The greatest common factor of 24 and 84 can be computed by using the least common multiple aka lcm of 24 and 84. This is the easiest approach:

gcf (24,84) = $\frac{24 \times 84}{lcm(24,84)} = \frac{2016}{168}$ = 12

Alternatively, the gcf of 24 and 84 can be found using the prime factorization of 24 and 84:

  • The prime factorization of 24 is: 2 x 2 x 2 x 3
  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • The prime factors and multiplicities 24 and 84 have in common are: 2 x 2 x 3
  • 2 x 2 x 3 is the gcf of 24 and 84
  • gcf(24,84) = 12

In any case, the easiest way to compute the gcf of two numbers like 24 and 84 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 24,84. The calculation is conducted automatically.

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

Use of GCF of 24 and 84

What is the greatest common factor of 24 and 84 used for? Answer: It is helpful for reducing fractions like 24 / 84. Just divide the nominator as well as the denominator by the gcf (24,84) to reduce the fraction to lowest terms.

$\frac{24}{84} = \frac{\frac{24}{12}}{\frac{84}{12}} = \frac{2}{7}$.

Properties of GCF of 24 and 84

The most important properties of the gcf(24,84) are:

  • Commutative property: gcf(24,84) = gcf(84,24)
  • Associative property: gcf(24,84,n) = gcf(gcf(84,24),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 24 and 84 is 12. In common notation: gcf (24,84) = 12.

If you have been searching for gcf 24 and 84 or gcf 24 84 then you have come to the correct page, too. The same is the true if you typed gcf for 24 and 84 in your favorite search engine.

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

Questions and comments related to the gcf of 24 and 84 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 24 and 84 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 factors of 252what is the prime factorization of 650what is prime factorization of 72prime factorization of 243prime factorization for 210is 105 a composite numberwhat is the greatest common factor of 72 and 96is 27 a prime number or compositegreatest common factor of 42 and 72what is the prime factorization of 46254 prime factorsprime factorization of 296what is the lcm of 2 and 76xtableprime factorization 2521 to 100 multiplication tableprime factorization for 65what is the greatest common factor of 84 and 96common multiples of 2 and 6prime factorization for 104prime factorization of 441what is the prime factorization of 210multiplication table 20x20 printableprime factorization of 48prime factorization of 114what is the greatest common factor of 42 and 48times table 30x30gcf of 28 and 42greatest prime factor of 38the prime factorization of 58highest common factor calculator 3 numbersprime factorization of 153multiplication table 90x90factor tree of 66prime factorization 39the prime factorization of 114write the prime factorization of 27is 251 a prime numbercommon multiples of 3 and 6multiplication chart to 20multiplication chart that goes to 100is 157 a prime numberwhat is the lcm of 7 and 5is 107 a composite numbermultiplication table up to 10000write the prime factorization of 50multiplication table of 60write the prime factorization of 56prime factors of 95prime factorization 110prime factorization of 297common multiples of 12 and 18gcf of 81 and 48the prime factorization of 6389 prime factorizationprime factor of 57prime factorization of 396is 161 a prime number127 is a prime numberwhat is the lcm of 3 and 6what is the lcm of 4 and 10prime factorization of 47is 57 a prime or composite numberprime factor of 65prime factorization 360gcf of 81 and 48determine the prime factorization of 88prime factor of 12875 as a product of prime factorsprime factorization of 176prime factorization of 129the prime factorization of 63multiplication chart to 300