GCF of 42 and 56


The gcf of 42 and 56 is the largest positive integer that divides the numbers 42 and 56 without a remainder. Spelled out, it is the greatest common factor of 42 and 56. Here you can find the gcf of 42 and 56, 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 56, but also that of three or more integers including forty-two and fifty-six for example. Keep reading to learn everything about the gcf (42,56) and the terms related to it.

What is the GCF of 42 and 56

If you just want to know what is the greatest common factor of 42 and 56, it is 14. Usually, this is written as

gcf(42,56) = 14

The gcf of 42 and 56 can be obtained like this:

  • The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1.
  • The factors of 56 are 56, 28, 14, 8, 7, 4, 2, 1.
  • The common factors of 42 and 56 are 14, 7, 2, 1, intersecting the two sets above.
  • In the intersection factors of 42 ∩ factors of 56 the greatest element is 14.
  • Therefore, the greatest common factor of 42 and 56 is 14.

Taking the above into account you also know how to find all the common factors of 42 and 56, not just the greatest. In the next section we show you how to calculate the gcf of forty-two and fifty-six by means of two more methods.

How to find the GCF of 42 and 56

The greatest common factor of 42 and 56 can be computed by using the least common multiple aka lcm of 42 and 56. This is the easiest approach:

gcf (42,56) = $\frac{42 \times 56}{lcm(42,56)} = \frac{2352}{168}$ = 14

Alternatively, the gcf of 42 and 56 can be found using the prime factorization of 42 and 56:

  • The prime factorization of 42 is: 2 x 3 x 7
  • The prime factorization of 56 is: 2 x 2 x 2 x 7
  • The prime factors and multiplicities 42 and 56 have in common are: 2 x 7
  • 2 x 7 is the gcf of 42 and 56
  • gcf(42,56) = 14

In any case, the easiest way to compute the gcf of two numbers like 42 and 56 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 42,56. The calculation is conducted automatically.

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

Use of GCF of 42 and 56

What is the greatest common factor of 42 and 56 used for? Answer: It is helpful for reducing fractions like 42 / 56. Just divide the nominator as well as the denominator by the gcf (42,56) to reduce the fraction to lowest terms.

$\frac{42}{56} = \frac{\frac{42}{14}}{\frac{56}{14}} = \frac{3}{4}$.

Properties of GCF of 42 and 56

The most important properties of the gcf(42,56) are:

  • Commutative property: gcf(42,56) = gcf(56,42)
  • Associative property: gcf(42,56,n) = gcf(gcf(56,42),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 56 is 14. In common notation: gcf (42,56) = 14.

If you have been searching for gcf 42 and 56 or gcf 42 56 then you have come to the correct page, too. The same is the true if you typed gcf for 42 and 56 in your favorite search engine.

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

Questions and comments related to the gcf of 42 and 56 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 56 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


multiplication table 40 x 40the prime factorization of 12048 as a product of prime factorsprime factors of 1050is 24 a composite or prime numberis 19 a prime or composite numberwhat are the prime factors of 132what is the greatest common factor of 72 and 45what is the greatest common factor of 72 and 81greatest common factor of 64 and 48what is the prime factorization of 83prime factorization of 400 using exponentsprime factor of 105prime factorization chart 1-100common multiples of 8 and 3multiplication chart 50prime factorization 240prime factors of 250lcm of 18 and 72what is the gcf of 100gcf of 17 and 85prime factorization of 276prime factorization of 675what is the prime factorization of 315prime factorization of 561definition of a prime factor7is7what is the prime factorization for 150hcf of 45 and 72what is the prime factorization of 70what is the greatest common factor of 63multiplication chart to 200prime factorization for 55prime factors of 440what is the prime factorization of 64gcf of 75 and 90the prime factorization of 11484 prime factorizationwhat is the prime factorization of 138gcf of 65prime factorization of 154gcf of 81 and 48what is the prime factorization of 97multiplication tables 1-30what is the prime factorization of 625100-78700 prime factorizationgcf of 26what is the greatest common factor of 56 and 64prime factorization of 170what is the greatest common factor of 34 and 51what is the prime factorization of 168greatest common factor of 39 and 52factorization of 175what is the prime factorization of 2800prime and composite numbers 1 200multiplication table 1-15prime factorization of 145gcf of 90 and 108the lcm of 2 and 4what is the greatest common factor of 54 and 63multiplication chart to 20prime factorization of 69prime factorization of 828the prime factorization of 102gcf of 81 and 64gcf of 56 and 63greatest common factor of 48 and 60highest common factor calculatorprime factorization of 176is 199 a prime numberis 21 a prime number or a composite number