# GCF of 72 and 60

The gcf of 72 and 60 is the largest positive integer that divides the numbers 72 and 60 without a remainder. Spelled out, it is the greatest common factor of 72 and 60. Here you can find the gcf of 72 and 60, 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 60, but also that of three or more integers including seventy-two and sixty for example. Keep reading to learn everything about the gcf (72,60) and the terms related to it.

## What is the GCF of 72 and 60

If you just want to know what is the greatest common factor of 72 and 60, it is 12. Usually, this is written as

gcf(72,60) = 12

The gcf of 72 and 60 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 60 are 60, 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1.
• The common factors of 72 and 60 are 12, 6, 4, 3, 2, 1, intersecting the two sets above.
• In the intersection factors of 72 ∩ factors of 60 the greatest element is 12.
• Therefore, the greatest common factor of 72 and 60 is 12.

Taking the above into account you also know how to find all the common factors of 72 and 60, not just the greatest. In the next section we show you how to calculate the gcf of seventy-two and sixty by means of two more methods.

## How to find the GCF of 72 and 60

The greatest common factor of 72 and 60 can be computed by using the least common multiple aka lcm of 72 and 60. This is the easiest approach:

gcf (72,60) = $\frac{72 \times 60}{lcm(72,60)} = \frac{4320}{360}$ = 12

Alternatively, the gcf of 72 and 60 can be found using the prime factorization of 72 and 60:

• The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
• The prime factorization of 60 is: 2 x 2 x 3 x 5
• The prime factors and multiplicities 72 and 60 have in common are: 2 x 2 x 3
• 2 x 2 x 3 is the gcf of 72 and 60
• gcf(72,60) = 12

In any case, the easiest way to compute the gcf of two numbers like 72 and 60 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 72,60. The calculation is conducted automatically.

The gcf is...
Similar searched terms on our site also include:

## Use of GCF of 72 and 60

What is the greatest common factor of 72 and 60 used for? Answer: It is helpful for reducing fractions like 72 / 60. Just divide the nominator as well as the denominator by the gcf (72,60) to reduce the fraction to lowest terms.

$\frac{72}{60} = \frac{\frac{72}{12}}{\frac{60}{12}} = \frac{6}{5}$.

## Properties of GCF of 72 and 60

The most important properties of the gcf(72,60) are:

• Commutative property: gcf(72,60) = gcf(60,72)
• Associative property: gcf(72,60,n) = gcf(gcf(60,72),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

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 60 is 12. In common notation: gcf (72,60) = 12.

If you have been searching for gcf 72 and 60 or gcf 72 60 then you have come to the correct page, too. The same is the true if you typed gcf for 72 and 60 in your favorite search engine.

Note that you can find the greatest common factor of many integer pairs including seventy-two / sixty by using the search form in the sidebar of this page.

Questions and comments related to the gcf of 72 and 60 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 72 and 60 has been useful to you, and make sure to bookmark our site.

Posted in Greatest Common Factor

## Related pages

is 21 a prime number or a composite numberprime factors of 66prime factors of 1050prime factorization of 230what is the prime factorization of 186the lcm of 3 and 5what is the prime factorization of 33list of prime factors 1 1000what is the gcf of 63is 86 a prime or composite numberwhat is the gcf of 44 and 66what is 42 as a product of prime factorswhat is the lcm of 10 and 548 as a product of prime factorswhat is the prime factorization of 180is 211 a prime number196 prime factorizationprime factorizations of 72prime factors of 130what is the prime factorization of 540gcf of 75 and 60prime factorization of 244what is the prime factorization of 875what is the prime factorization of 310write the prime factorization of 36what is the prime factorization of 293greatest common factor of 48 and 64what is the prime factorization of 250what is the prime factorization of 56what are the prime factors of 125factor tree of 66700 prime factorization4x times tablesprime factors of 294what is the greatest prime factor of 96what is the prime factorization of 189prime factorization 85multiplication chart 1 300find the prime factorization of 85greatest common factor of 54 and 72what is the gcf of 84what is the lcm of 3 and 108x tablesprime factors of 66multiplication tables to 100multiplication tables 1-30lcm of 150express 96 as a product of prime factors126 prime factorizationwhat is the prime factorization of 249prime factorization 66gcf of 48 and 64multiplication table 1-20 printableprime factorization 588multiplication table upto 30is 158 a prime number100-36common multiples of 10prime factorization of 212common multiples of 2 3 and 5is 57 a prime or composite numbereasiest way to find lcmwhat is the prime factorization of 78what are the prime factors of 132multiplication table of 42common multiples of 2 3 and 4prime factorization for 144prime factorization of 648prime factor of 91multiplication chart up to 300common multiples of 9 and 12