The gcf of 88 and 31 is the largest positive integer that divides the numbers 88 and 31 without a remainder. Spelled out, it is the greatest common factor of 88 and 31. Here you can find the gcf of 88 and 31, along with a total of three methods for computing it.
What is the GCF of 88 and 31
If you just want to know what is the greatest common factor of 88 and 31, it is 1. Usually, this is written as
The gcf of 88 and 31 can be obtained like this:
- The factors of 88 are 88, 44, 22, 11, 8, 4, 2, 1.
- The factors of 31 are 31, 1.
- The common factors of 88 and 31 are 1, intersecting the two sets above.
- In the intersection factors of 88 ∩ factors of 31 the greatest element is 1.
- Therefore, the greatest common factor of 88 and 31 is 1.
Taking the above into account you also know how to find all the common factors of 88 and 31, not just the greatest. In the next section we show you how to calculate the gcf of eighty-eight and thirty-one by means of two more methods.
How to find the GCF of 88 and 31
The greatest common factor of 88 and 31 can be computed by using the least common multiple aka lcm of 88 and 31. This is the easiest approach:
Alternatively, the gcf of 88 and 31 can be found using the prime factorization of 88 and 31:
- The prime factorization of 88 is: 2 x 2 x 2 x 11
- The prime factorization of 31 is: 31
- The prime factors and multiplicities 88 and 31 have in common are: 1
- 1 is the gcf of 88 and 31
- gcf(88,31) = 1
In any case, the easiest way to compute the gcf of two numbers like 88 and 31 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 88,31. The calculation is conducted automatically.
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Use of GCF of 88 and 31
What is the greatest common factor of 88 and 31 used for? Answer: It is helpful for reducing fractions like 88 / 31. Just divide the nominator as well as the denominator by the gcf (88,31) to reduce the fraction to lowest terms.
Properties of GCF of 88 and 31
The most important properties of the gcf(88,31) are:
- Commutative property: gcf(88,31) = gcf(31,88)
- Associative property: gcf(88,31,n) = gcf(gcf(31,88),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 88 and 31 is 1. In common notation: gcf (88,31) = 1.
If you have been searching for gcf 88 and 31 or gcf 88 31 then you have come to the correct page, too. The same is the true if you typed gcf for 88 and 31 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including eighty-eight / thirty-one by using the search form in the sidebar of this page.
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