The gcf of 16 and 70 is the largest positive integer that divides the numbers 16 and 70 without a remainder. Spelled out, it is the greatest common factor of 16 and 70. Here you can find the gcf of 16 and 70, along with a total of three methods for computing it.
What is the GCF of 16 and 70
If you just want to know what is the greatest common factor of 16 and 70, it is 2. Usually, this is written as
The gcf of 16 and 70 can be obtained like this:
- The factors of 16 are 16, 8, 4, 2, 1.
- The factors of 70 are 70, 35, 14, 10, 7, 5, 2, 1.
- The common factors of 16 and 70 are 2, 1, intersecting the two sets above.
- In the intersection factors of 16 ∩ factors of 70 the greatest element is 2.
- Therefore, the greatest common factor of 16 and 70 is 2.
Taking the above into account you also know how to find all the common factors of 16 and 70, not just the greatest. In the next section we show you how to calculate the gcf of sixteen and seventy by means of two more methods.
How to find the GCF of 16 and 70
The greatest common factor of 16 and 70 can be computed by using the least common multiple aka lcm of 16 and 70. This is the easiest approach:
Alternatively, the gcf of 16 and 70 can be found using the prime factorization of 16 and 70:
- The prime factorization of 16 is: 2 x 2 x 2 x 2
- The prime factorization of 70 is: 2 x 5 x 7
- The prime factors and multiplicities 16 and 70 have in common are: 2
- 2 is the gcf of 16 and 70
- gcf(16,70) = 2
In any case, the easiest way to compute the gcf of two numbers like 16 and 70 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 16,70. The calculation is conducted automatically.
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Use of GCF of 16 and 70
What is the greatest common factor of 16 and 70 used for? Answer: It is helpful for reducing fractions like 16 / 70. Just divide the nominator as well as the denominator by the gcf (16,70) to reduce the fraction to lowest terms.
Properties of GCF of 16 and 70
The most important properties of the gcf(16,70) are:
- Commutative property: gcf(16,70) = gcf(70,16)
- Associative property: gcf(16,70,n) = gcf(gcf(70,16),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 16 and 70 is 2. In common notation: gcf (16,70) = 2.
If you have been searching for gcf 16 and 70 or gcf 16 70 then you have come to the correct page, too. The same is the true if you typed gcf for 16 and 70 in your favorite search engine.
Note that you can find the greatest common factor of many integer pairs including sixteen / seventy by using the search form in the sidebar of this page.
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