GCF of 42 and 72


The gcf of 42 and 72 is the largest positive integer that divides the numbers 42 and 72 without a remainder. Spelled out, it is the greatest common factor of 42 and 72. Here you can find the gcf of 42 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 42 and 72, but also that of three or more integers including forty-two and seventy-two for example. Keep reading to learn everything about the gcf (42,72) and the terms related to it.

What is the GCF of 42 and 72

If you just want to know what is the greatest common factor of 42 and 72, it is 6. Usually, this is written as

gcf(42,72) = 6

The gcf of 42 and 72 can be obtained like this:

  • The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1.
  • The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1.
  • The common factors of 42 and 72 are 6, 3, 2, 1, intersecting the two sets above.
  • In the intersection factors of 42 ∩ factors of 72 the greatest element is 6.
  • Therefore, the greatest common factor of 42 and 72 is 6.

Taking the above into account you also know how to find all the common factors of 42 and 72, not just the greatest. In the next section we show you how to calculate the gcf of forty-two and seventy-two by means of two more methods.

How to find the GCF of 42 and 72

The greatest common factor of 42 and 72 can be computed by using the least common multiple aka lcm of 42 and 72. This is the easiest approach:

gcf (42,72) = $\frac{42 \times 72}{lcm(42,72)} = \frac{3024}{504}$ = 6

Alternatively, the gcf of 42 and 72 can be found using the prime factorization of 42 and 72:

  • The prime factorization of 42 is: 2 x 3 x 7
  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • The prime factors and multiplicities 42 and 72 have in common are: 2 x 3
  • 2 x 3 is the gcf of 42 and 72
  • gcf(42,72) = 6

In any case, the easiest way to compute the gcf of two numbers like 42 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 42,72. The calculation is conducted automatically.

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

Use of GCF of 42 and 72

What is the greatest common factor of 42 and 72 used for? Answer: It is helpful for reducing fractions like 42 / 72. Just divide the nominator as well as the denominator by the gcf (42,72) to reduce the fraction to lowest terms.

$\frac{42}{72} = \frac{\frac{42}{6}}{\frac{72}{6}} = \frac{7}{12}$.

Properties of GCF of 42 and 72

The most important properties of the gcf(42,72) are:

  • Commutative property: gcf(42,72) = gcf(72,42)
  • Associative property: gcf(42,72,n) = gcf(gcf(72,42),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 42 and 72 is 6. In common notation: gcf (42,72) = 6.

If you have been searching for gcf 42 and 72 or gcf 42 72 then you have come to the correct page, too. The same is the true if you typed gcf for 42 and 72 in your favorite search engine.

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

Questions and comments related to the gcf of 42 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 42 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


find the prime factorization of 84prime factorization of 196lcm of 150what is the lcm of 2 and 4what is the prime factorization of 52prime factorization 6720x multiplication tablewhat is the prime factorization of 135find the prime factorization of 200prime factors of 210is 211 a prime numberwhat is the lcm ofprime factorization for 76whats the prime factorization of 63what is the gcf of 35 and 63prime factorization of 216greatest common factor of 35 and 36is 211 a prime numberwhat is the prime factorization of 20whats a prime factorprime numbers 1-60multiples of tenis 24 a prime number or a composite numberwhat is the prime factorization of 484what is the greatest prime factor of 38what is the gcf of 96 48 and 84what is the prime factorization of 126lcm and gcf finderwhat is the prime factorization of 112what is the gcf of 6multiplication chart to 200prime factorization for 60is 247 a prime numberwhat is the prime factors of 81prime factorization 7584 as a product of prime factorsis 86 a prime or composite numberwhat is the greatest common factor of 70 and 42is 253 a prime numberthe prime factorization of 90prime factors of 540prime factorization of 10236-28-36multiplication table 1-13what is the lcm of 4 and 6find the prime factorization of 8538-26-38write the prime factorization of 40prime factorization of 1700prime factorization for 72lowest common multiple of 60 and 96the multiplication table up to 100what are the prime factors of 65multiples of elevenwhat is the prime factorization of 7270 prime factorizationmultiplication table chart 1 3048 prime factorizationwhat is the prime factorization of 76sevens times tablesgcf and lcm of 36 and 4542 prime factorizationwhat are the prime factors of 64prime factorization 57what is the prime factorization of 100063 prime factorizationcommon multiples of 7 and 8prime factors of 315is 24 a prime number or a composite numbergreatest common factor chartgreatest common factor of 72 and 108prime factor of 99greatest common factor of 36 and 44prime factorization of 380common denominator of 5 and 8prime factors of numbers 1 100100-55prime factorization 125