The gcf of 35 and 10 is the largest positive integer that divides the numbers 35 and 10 without a remainder. Spelled out, it is the greatest common factor of 35 and 10. Here you can find the gcf of 35 and 10, along with a total of three methods for computing it.
What is the GCF of 35 and 10
If you just want to know what is the greatest common factor of 35 and 10, it is 5. Usually, this is written as
The gcf of 35 and 10 can be obtained like this:
- The factors of 35 are 35, 7, 5, 1.
- The factors of 10 are 10, 5, 2, 1.
- The common factors of 35 and 10 are 5, 1, intersecting the two sets above.
- In the intersection factors of 35 ∩ factors of 10 the greatest element is 5.
- Therefore, the greatest common factor of 35 and 10 is 5.
Taking the above into account you also know how to find all the common factors of 35 and 10, not just the greatest. In the next section we show you how to calculate the gcf of thirty-five and ten by means of two more methods.
How to find the GCF of 35 and 10
The greatest common factor of 35 and 10 can be computed by using the least common multiple aka lcm of 35 and 10. This is the easiest approach:
Alternatively, the gcf of 35 and 10 can be found using the prime factorization of 35 and 10:
- The prime factorization of 35 is: 5 x 7
- The prime factorization of 10 is: 2 x 5
- The prime factors and multiplicities 35 and 10 have in common are: 5
- 5 is the gcf of 35 and 10
- gcf(35,10) = 5
In any case, the easiest way to compute the gcf of two numbers like 35 and 10 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 35,10. The calculation is conducted automatically.
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Use of GCF of 35 and 10
What is the greatest common factor of 35 and 10 used for? Answer: It is helpful for reducing fractions like 35 / 10. Just divide the nominator as well as the denominator by the gcf (35,10) to reduce the fraction to lowest terms.
Properties of GCF of 35 and 10
The most important properties of the gcf(35,10) are:
- Commutative property: gcf(35,10) = gcf(10,35)
- Associative property: gcf(35,10,n) = gcf(gcf(10,35),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 35 and 10 is 5. In common notation: gcf (35,10) = 5.
If you have been searching for gcf 35 and 10 or gcf 35 10 then you have come to the correct page, too. The same is the true if you typed gcf for 35 and 10 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including thirty-five / ten by using the search form in the sidebar of this page.
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