The gcf of 72 and 64 is the largest positive integer that divides the numbers 72 and 64 without a remainder. Spelled out, it is the greatest common factor of 72 and 64. Here you can find the gcf of 72 and 64, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 72 and 64, but also that of three or more integers including seventy-two and sixty-four for example. Keep reading to learn everything about the gcf (72,64) and the terms related to it.
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What is the GCF of 72 and 64
If you just want to know what is the greatest common factor of 72 and 64, it is 8. Usually, this is written asgcf(72,64) = 8
The gcf of 72 and 64 can be obtained like this:The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1. The factors of 64 are 64, 32, 16, 8, 4, 2, 1. The common factors of 72 and 64 are 8, 4, 2, 1, intersecting the two sets above. In the intersection factors of 72 ∩ factors of 64 the greatest element is 8. Therefore, the greatest common factor of 72 and 64 is 8.
Taking the above into account you also know how to find all the common factors of 72 and 64, not just the greatest. In the next section we show you how to calculate the gcf of seventy-two and sixty-four by means of two more methods.
How to find the GCF of 72 and 64
The greatest common factor of 72 and 64 can be computed by using the least common multiple aka lcm of 72 and 64. This is the easiest approach:
gcf (72,64) = frac72 imes 64lcm(72,64) = frac4608576 = 8
Alternatively, the gcf of 72 and 64 can be found using the prime factorization of 72 and 64:The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3 The prime factorization of 64 is: 2 x 2 x 2 x 2 x 2 x 2 The prime factors and multiplicities 72 and 64 have in common are: 2 x 2 x 2 2 x 2 x 2 is the gcf of 72 and 64 gcf(72,64) = 8
In any case, the easiest way to compute the gcf of two numbers like 72 and 64 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 72,64. The calculation is conducted automatically.
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Use of GCF of 72 and 64
What is the greatest common factor of 72 and 64 used for? Answer: It is helpful for reducing fractions like 72 / 64. Just divide the nominator as well as the denominator by the gcf (72,64) to reduce the fraction to lowest terms.
frac7264 = fracfrac728frac648 = frac98.
Properties of GCF of 72 and 64
The most important properties of the gcf(72,64) are:Commutative property: gcf(72,64) = gcf(64,72) Associative property: gcf(72,64,n) = gcf(gcf(64,72),n) n eq 0 hinspacein hinspacemathbbZ
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 72 and 64 is 8. In common notation: gcf (72,64) = 8.
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Note that you can find the greatest common factor of many integer pairs including seventy-two / sixty-four by using the search form in the sidebar of this page.
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