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