The gcf of 14 and 65 is the largest positive integer that divides the numbers 14 and 65 without a remainder. Spelled out, it is the greatest common factor of 14 and 65. Here you can find the gcf of 14 and 65, along with a total of three methods for computing it.
What is the GCF of 14 and 65
If you just want to know what is the greatest common factor of 14 and 65, it is 1. Usually, this is written as
The gcf of 14 and 65 can be obtained like this:
- The factors of 14 are 14, 7, 2, 1.
- The factors of 65 are 65, 13, 5, 1.
- The common factors of 14 and 65 are 1, intersecting the two sets above.
- In the intersection factors of 14 ∩ factors of 65 the greatest element is 1.
- Therefore, the greatest common factor of 14 and 65 is 1.
Taking the above into account you also know how to find all the common factors of 14 and 65, not just the greatest. In the next section we show you how to calculate the gcf of fourteen and sixty-five by means of two more methods.
How to find the GCF of 14 and 65
The greatest common factor of 14 and 65 can be computed by using the least common multiple aka lcm of 14 and 65. This is the easiest approach:
Alternatively, the gcf of 14 and 65 can be found using the prime factorization of 14 and 65:
- The prime factorization of 14 is: 2 x 7
- The prime factorization of 65 is: 5 x 13
- The prime factors and multiplicities 14 and 65 have in common are: 1
- 1 is the gcf of 14 and 65
- gcf(14,65) = 1
In any case, the easiest way to compute the gcf of two numbers like 14 and 65 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 14,65. The calculation is conducted automatically.
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Use of GCF of 14 and 65
What is the greatest common factor of 14 and 65 used for? Answer: It is helpful for reducing fractions like 14 / 65. Just divide the nominator as well as the denominator by the gcf (14,65) to reduce the fraction to lowest terms.
Properties of GCF of 14 and 65
The most important properties of the gcf(14,65) are:
- Commutative property: gcf(14,65) = gcf(65,14)
- Associative property: gcf(14,65,n) = gcf(gcf(65,14),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 14 and 65 is 1. In common notation: gcf (14,65) = 1.
If you have been searching for gcf 14 and 65 or gcf 14 65 then you have come to the correct page, too. The same is the true if you typed gcf for 14 and 65 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including fourteen / sixty-five by using the search form in the sidebar of this page.
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