GCF of 84 and 90


The gcf of 84 and 90 is the largest positive integer that divides the numbers 84 and 90 without a remainder. Spelled out, it is the greatest common factor of 84 and 90. Here you can find the gcf of 84 and 90, 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 84 and 90, but also that of three or more integers including eighty-four and ninety for example. Keep reading to learn everything about the gcf (84,90) and the terms related to it.

What is the GCF of 84 and 90

If you just want to know what is the greatest common factor of 84 and 90, it is 6. Usually, this is written as

gcf(84,90) = 6

The gcf of 84 and 90 can be obtained like this:

  • The factors of 84 are 84, 42, 28, 21, 14, 12, 7, 6, 4, 3, 2, 1.
  • The factors of 90 are 90, 45, 30, 18, 15, 10, 9, 6, 5, 3, 2, 1.
  • The common factors of 84 and 90 are 6, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 84 ∩ factors of 90 the greatest element is 6.
  • Therefore, the greatest common factor of 84 and 90 is 6.

Taking the above into account you also know how to find all the common factors of 84 and 90, not just the greatest. In the next section we show you how to calculate the gcf of eighty-four and ninety by means of two more methods.

How to find the GCF of 84 and 90

The greatest common factor of 84 and 90 can be computed by using the least common multiple aka lcm of 84 and 90. This is the easiest approach:

gcf (84,90) = $\frac{84 \times 90}{lcm(84,90)} = \frac{7560}{1260}$ = 6

Alternatively, the gcf of 84 and 90 can be found using the prime factorization of 84 and 90:

  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • The prime factorization of 90 is: 2 x 3 x 3 x 5
  • The prime factors and multiplicities 84 and 90 have in common are: 2 x 3
  • 2 x 3 is the gcf of 84 and 90
  • gcf(84,90) = 6

In any case, the easiest way to compute the gcf of two numbers like 84 and 90 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 84,90. The calculation is conducted automatically.

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

Use of GCF of 84 and 90

What is the greatest common factor of 84 and 90 used for? Answer: It is helpful for reducing fractions like 84 / 90. Just divide the nominator as well as the denominator by the gcf (84,90) to reduce the fraction to lowest terms.

$\frac{84}{90} = \frac{\frac{84}{6}}{\frac{90}{6}} = \frac{14}{15}$.

Properties of GCF of 84 and 90

The most important properties of the gcf(84,90) are:

  • Commutative property: gcf(84,90) = gcf(90,84)
  • Associative property: gcf(84,90,n) = gcf(gcf(90,84),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 84 and 90 is 6. In common notation: gcf (84,90) = 6.

If you have been searching for gcf 84 and 90 or gcf 84 90 then you have come to the correct page, too. The same is the true if you typed gcf for 84 and 90 in your favorite search engine.

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

Questions and comments related to the gcf of 84 and 90 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 84 and 90 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 factor of 65prime factorization of 83the prime factorization of 300multiplication table 1-20prime factorization for 56what is prime factorization of 52write the number 99 as a product of prime factorsprime factorization 19875 prime factorizationprime factorization 64what is the prime factorization for 44find the prime factorization of 34gcf of 70 and 98prime factorization of 85what is the prime factorization for 56factorization of 196highest common factor of 72 and 96prime factors of 112find the greatest common factor of 270 and 360common multiples of 12prime factorization 300common multiples of 7 and 9what is the prime factorization of 248prime factorization of 490prime factors of 140what is the prime factorization of 175what is the prime factorization of 52prime factor of 57is 143 a prime numberwrite 78 as a product of prime factorsprime factorization of 504prime factorization 48prime factorization of 44prime factorization of 1249times tableprime factorization 162what is the prime factorization of 39write the prime factorization of 60what is the prime factorization of 196greatest common factor of 54 and 72what is the prime factors of 90common multiples of 10prime factors of 112prime factors of 65prime factors of 405multiplication table 1-15prime factors of 700what is the greatest common factor of 42 and 70prime factorization of 62what is the prime factorization of 875multiplication table to 300is 14 a prime or composite numbercommon multiples of 15prime factorization of 310prime factorization 200find the greatest common factor of 16 and 36what is the prime factorization of 285the prime factorization of 144what is the lcm of 6 12 and 15is 24 a composite or prime number37-100what is the prime factorization of 78prime factorization of 83the prime factorization of 84prime factorization of 8438-26-38factorization of 126what is the prime factorization of 79prime factors of 91100-72easiest way to find greatest common factorwhat is the greatest common factor of 35 and 63gcf of 48 and 72what is the lcm of 4 and 6is 107 a composite number