# 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.

Posted in Greatest Common Factor

## Related pages

what is the prime factorization of 484prime factorization of 190060 prime factorizationmultiplication table that goes up to 20what is the lcm of 6 and 3the lcm of 3 and 4write 18 as a product of prime factorsmultiplication table 30 x 30prime factorization for 66what is the prime factorization of 153what is the prime factorization of 198greatest common factor of 28 and 70prime factorization for 8what is the prime factorization of 55what are the prime factors of 81write 600 as a product of its prime factorswhat is the gcf of 81 and 36prime factorization of 139greatest common factor of 72 and 96factor tree of 84prime factorization 55highest common factor of 14 and 49prime factorization of 630what is the lcm of 2 and 10prime factorization of 375prime factorization for 8greatest prime factor of 68what is the lcm of 2 and 4what are the prime factors of 64prime factorization 147what is the gcf of 6lowest common multiple of 60 and 9660 multiplication tablewhat is the lcm of 3find the prime factorization of 34prime factorization of 264what is the prime factorization of 210prime factorization for 46is 185 a prime numberwhat is the lcm of 2 and 12gcf of 40 and 64greatest common factor of 14 and 49what is the prime factorization for 81what is the prime factorization of 1000prime factorization of 255factor tree of 66greatest common factor of 36 and 44prime factorization of 114prime factorization of 630prime factorization of 152multiplication table up to 10000is 68 a prime or composite numberprime factors of 220common multiples of 5 and 6easiest way to find lcmprime factorization of 196multiplication table 40x40gcf of 75 and 60what is the greatest common factor of 17 and 34is 143 a prime numberprime factorization of 169gcf monomial calculatoris 158 a prime numberprime factorization 75the prime factorization of 51what is the lcm of 4 and 10what is the prime factorization of 289common denominator of 7 and 12easiest way to find greatest common factormultiplication table printable 20x20multiplication table 13 to 20is 63 a prime or composite numberprime factorization for 240what are the prime factors of 57what is the greatest common factor of 24 and 36what are the prime factors of 81prime factorization of 42 using exponentswhat is the greatest common factor of 18 and 63