The gcf of 5 and 40 is the largest positive integer that divides the numbers 5 and 40 without a remainder. Spelled out, it is the greatest common factor of 5 and 40. Here you can find the gcf of 5 and 40, along with a total of three methods for computing it.
What is the GCF of 5 and 40
If you just want to know what is the greatest common factor of 5 and 40, it is 5. Usually, this is written as
The gcf of 5 and 40 can be obtained like this:
- The factors of 5 are 5, 1.
- The factors of 40 are 40, 20, 10, 8, 5, 4, 2, 1.
- The common factors of 5 and 40 are 5, 1, intersecting the two sets above.
- In the intersection factors of 5 ∩ factors of 40 the greatest element is 5.
- Therefore, the greatest common factor of 5 and 40 is 5.
Taking the above into account you also know how to find all the common factors of 5 and 40, not just the greatest. In the next section we show you how to calculate the gcf of five and forty by means of two more methods.
How to find the GCF of 5 and 40
The greatest common factor of 5 and 40 can be computed by using the least common multiple aka lcm of 5 and 40. This is the easiest approach:
Alternatively, the gcf of 5 and 40 can be found using the prime factorization of 5 and 40:
- The prime factorization of 5 is: 5
- The prime factorization of 40 is: 2 x 2 x 2 x 5
- The prime factors and multiplicities 5 and 40 have in common are: 5
- 5 is the gcf of 5 and 40
- gcf(5,40) = 5
In any case, the easiest way to compute the gcf of two numbers like 5 and 40 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 5,40. The calculation is conducted automatically.
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Use of GCF of 5 and 40
What is the greatest common factor of 5 and 40 used for? Answer: It is helpful for reducing fractions like 5 / 40. Just divide the nominator as well as the denominator by the gcf (5,40) to reduce the fraction to lowest terms.
Properties of GCF of 5 and 40
The most important properties of the gcf(5,40) are:
- Commutative property: gcf(5,40) = gcf(40,5)
- Associative property: gcf(5,40,n) = gcf(gcf(40,5),n)
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 5 and 40 is 5. In common notation: gcf (5,40) = 5.
If you have been searching for gcf 5 and 40 or gcf 5 40 then you have come to the correct page, too. The same is the true if you typed gcf for 5 and 40 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including five / forty by using the search form in the sidebar of this page.
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