The gcf of 38 and 80 is the largest positive integer that divides the numbers 38 and 80 without a remainder. Spelled out, it is the greatest common factor of 38 and 80. Here you can find the gcf of 38 and 80, along with a total of three methods for computing it.
What is the GCF of 38 and 80
If you just want to know what is the greatest common factor of 38 and 80, it is 2. Usually, this is written as
The gcf of 38 and 80 can be obtained like this:
- The factors of 38 are 38, 19, 2, 1.
- The factors of 80 are 80, 40, 20, 16, 10, 8, 5, 4, 2, 1.
- The common factors of 38 and 80 are 2, 1, intersecting the two sets above.
- In the intersection factors of 38 ∩ factors of 80 the greatest element is 2.
- Therefore, the greatest common factor of 38 and 80 is 2.
Taking the above into account you also know how to find all the common factors of 38 and 80, not just the greatest. In the next section we show you how to calculate the gcf of thirty-eight and eighty by means of two more methods.
How to find the GCF of 38 and 80
The greatest common factor of 38 and 80 can be computed by using the least common multiple aka lcm of 38 and 80. This is the easiest approach:
Alternatively, the gcf of 38 and 80 can be found using the prime factorization of 38 and 80:
- The prime factorization of 38 is: 2 x 19
- The prime factorization of 80 is: 2 x 2 x 2 x 2 x 5
- The prime factors and multiplicities 38 and 80 have in common are: 2
- 2 is the gcf of 38 and 80
- gcf(38,80) = 2
In any case, the easiest way to compute the gcf of two numbers like 38 and 80 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 38,80. The calculation is conducted automatically.
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Use of GCF of 38 and 80
What is the greatest common factor of 38 and 80 used for? Answer: It is helpful for reducing fractions like 38 / 80. Just divide the nominator as well as the denominator by the gcf (38,80) to reduce the fraction to lowest terms.
Properties of GCF of 38 and 80
The most important properties of the gcf(38,80) are:
- Commutative property: gcf(38,80) = gcf(80,38)
- Associative property: gcf(38,80,n) = gcf(gcf(80,38),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 38 and 80 is 2. In common notation: gcf (38,80) = 2.
If you have been searching for gcf 38 and 80 or gcf 38 80 then you have come to the correct page, too. The same is the true if you typed gcf for 38 and 80 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including thirty-eight / eighty by using the search form in the sidebar of this page.
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