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The gcf of 91 and 7 is the largest positive integer that divides the numbers 91 and 7 without a remainder. Spelled out, it is the greatest common factor of 91 and 7. Here you can find the gcf of 91 and 7, along with a total of three methods for computing it.
What is the GCF of 91 and 7
If you just want to know what is the greatest common factor of 91 and 7, it is 7. Usually, this is written as
The gcf of 91 and 7 can be obtained like this:
- The factors of 91 are 91, 13, 7, 1.
- The factors of 7 are 7, 1.
- The common factors of 91 and 7 are 7, 1, intersecting the two sets above.
- In the intersection factors of 91 ∩ factors of 7 the greatest element is 7.
- Therefore, the greatest common factor of 91 and 7 is 7.
Taking the above into account you also know how to find all the common factors of 91 and 7, not just the greatest. In the next section we show you how to calculate the gcf of ninety-one and seven by means of two more methods.
How to find the GCF of 91 and 7
The greatest common factor of 91 and 7 can be computed by using the least common multiple aka lcm of 91 and 7. This is the easiest approach:
Alternatively, the gcf of 91 and 7 can be found using the prime factorization of 91 and 7:
- The prime factorization of 91 is: 7 x 13
- The prime factorization of 7 is: 7
- The prime factors and multiplicities 91 and 7 have in common are: 7
- 7 is the gcf of 91 and 7
- gcf(91,7) = 7
In any case, the easiest way to compute the gcf of two numbers like 91 and 7 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 91,7. The calculation is conducted automatically.
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Use of GCF of 91 and 7
What is the greatest common factor of 91 and 7 used for? Answer: It is helpful for reducing fractions like 91 / 7. Just divide the nominator as well as the denominator by the gcf (91,7) to reduce the fraction to lowest terms.
Properties of GCF of 91 and 7
The most important properties of the gcf(91,7) are:
- Commutative property: gcf(91,7) = gcf(7,91)
- Associative property: gcf(91,7,n) = gcf(gcf(7,91),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 91 and 7 is 7. In common notation: gcf (91,7) = 7.
If you have been searching for gcf 91 and 7 or gcf 91 7 then you have come to the correct page, too. The same is the true if you typed gcf for 91 and 7 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including ninety-one / seven by using the search form in the sidebar of this page.
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