GCF of 40 and 70


The gcf of 40 and 70 is the largest positive integer that divides the numbers 40 and 70 without a remainder. Spelled out, it is the greatest common factor of 40 and 70. Here you can find the gcf of 40 and 70, 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 40 and 70, but also that of three or more integers including forty and seventy for example. Keep reading to learn everything about the gcf (40,70) and the terms related to it.

What is the GCF of 40 and 70

If you just want to know what is the greatest common factor of 40 and 70, it is 10. Usually, this is written as

gcf(40,70) = 10

The gcf of 40 and 70 can be obtained like this:

  • The factors of 40 are 40, 20, 10, 8, 5, 4, 2, 1.
  • The factors of 70 are 70, 35, 14, 10, 7, 5, 2, 1.
  • The common factors of 40 and 70 are 10, 5, 2, 1, intersecting the two sets above.
  • In the intersection factors of 40 ∩ factors of 70 the greatest element is 10.
  • Therefore, the greatest common factor of 40 and 70 is 10.

Taking the above into account you also know how to find all the common factors of 40 and 70, not just the greatest. In the next section we show you how to calculate the gcf of forty and seventy by means of two more methods.

How to find the GCF of 40 and 70

The greatest common factor of 40 and 70 can be computed by using the least common multiple aka lcm of 40 and 70. This is the easiest approach:

gcf (40,70) = $\frac{40 \times 70}{lcm(40,70)} = \frac{2800}{280}$ = 10

Alternatively, the gcf of 40 and 70 can be found using the prime factorization of 40 and 70:

  • The prime factorization of 40 is: 2 x 2 x 2 x 5
  • The prime factorization of 70 is: 2 x 5 x 7
  • The prime factors and multiplicities 40 and 70 have in common are: 2 x 5
  • 2 x 5 is the gcf of 40 and 70
  • gcf(40,70) = 10

In any case, the easiest way to compute the gcf of two numbers like 40 and 70 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 40,70. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 40 and 70

What is the greatest common factor of 40 and 70 used for? Answer: It is helpful for reducing fractions like 40 / 70. Just divide the nominator as well as the denominator by the gcf (40,70) to reduce the fraction to lowest terms.

$\frac{40}{70} = \frac{\frac{40}{10}}{\frac{70}{10}} = \frac{4}{7}$.

Properties of GCF of 40 and 70

The most important properties of the gcf(40,70) are:

  • Commutative property: gcf(40,70) = gcf(70,40)
  • Associative property: gcf(40,70,n) = gcf(gcf(70,40),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 40 and 70 is 10. In common notation: gcf (40,70) = 10.

If you have been searching for gcf 40 and 70 or gcf 40 70 then you have come to the correct page, too. The same is the true if you typed gcf for 40 and 70 in your favorite search engine.

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

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