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The gcf of 91 and 31 is the largest positive integer that divides the numbers 91 and 31 without a remainder. Spelled out, it is the greatest common factor of 91 and 31. Here you can find the result for 91 and 31, along with a total of three methods for computing it.
What is the Greatest Common Factor of 91 and 31?
If you just want to know what is the greatest common factor of 91 and 31, it is 1. Usually, this is written as
The gcf of 91 and 31 can be obtained like this:
- The factors of 91 are 91, 13, 7, 1.
- The factors of 31 are 31, 1.
- The common factors of 91 and 31 are 1, intersecting the two sets above.
- In the intersection factors of 91 ∩ factors of 31 the greatest element is 1.
- Therefore, the greatest common factor of 91 and 31 is 1.
Taking the above into account you also know how to find all the common factors of 91 and 31, not just the greatest. In the next section we show you how to calculate the gcf of ninety-one and thirty-one by means of two more methods.
How to find the GCF of 91 and 31
The greatest common factor of 91 and 31 can be computed by using the least common multiple aka lcm of 91 and 31. This is the easiest approach:
Alternatively, the gcf of 91 and 31 can be found using the prime factorization of 91 and 31:
- The prime factorization of 91 is: 7 x 13
- The prime factorization of 31 is: 31
- The prime factors and multiplicities 91 and 31 have in common are: 1
- 1 is the gcf of 91 and 31
- gcf(91,31) = 1
In any case, the easiest way to compute the result for two numbers like 91 and 31 is by using our calculator above. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 91,31. The calculation is conducted automatically.
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In the next paragraph we explain how the mathematical concept can be employed.
Keep reading – it’s really interesting.
Use of Greatest Common Factor of 91 and 31
What is the greatest common factor of 91 and 31 used for? Answer: It is helpful for reducing fractions like 91 / 31. Just divide the nominator as well as the denominator by the gcf (91,31) to reduce the fraction to lowest terms.
Next, we shed a light on the mathematical properties.
Properties of GCF of 91 and 31
The most important properties of the gcf(91,31) are:
- Commutative property: gcf(91,31) = gcf(31,91)
- Associative property: gcf(91,31,n) = gcf(gcf(31,91),n)
The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.
Note that you can find the greatest common factor of many integer pairs including ninety-one / thirty-one by using the search form in the sidebar of this page.
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