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


prime factorization 77common multiples of 5 and 6continuous division method gcflist the prime factors of 42what is the lcm of 4gcf of 40 and 64what is the prime factorization of 175what is the prime factorization of 43what are the prime factors of 102prime factorization for 216multiplication table 30x30 pdfprime factorization of 123factorization of 126what is prime factorization of 120is 105 a prime number34-24-34prime factorization of 345nines times tablesis 105 a prime numberprime factorization of 147easiest way to find greatest common factorhcf of 60 and 75what is the prime factorization of 58what is the prime factorization of 450is 113 a prime numbergcf of 48 and 72prime factorization of 450prime factorization for 70prime factorization of 882gcf of 49 and 81greatest common factor of 28 and 70prime factorization 75gcf of 56 and 63is 179 a prime numberprime factors of 300what is the prime factorization of 20common multiples of 3 and 5times table 25x25prime factorization 80multiplication tables 1-20multiplication table up to 1000what is the prime factorization of 248prime factorization of 540is 147 a prime numberfinding the gcf calculatorwhat is the gcf of 84prime factors of 700prime factorization of 684prime factorization 162100-36hcf of 45 and 72953 prime numberdefinition of a prime factorlcm of 120 and 150lcm 5 7what is prime factorization of 120prime factorization for 44is 229 a prime numberdivisors of 496what are the prime factors of 625greatest common factor of 39 and 52prime factorization for 38the lcm of 2 and 4prime factorization of 2200lowest common multiple of 72 and 120prime factorization 245prime factorization of 28912 x 12 multiplication tablecommon multiples of 10find the prime factorization of 52prime factorization of 95prime factorization 38multiplication chart to 25prime factorization of 345prime factorization 350what are the prime factors of 294