Calculate GCF, GCD and HCF of a set of two or more numbers and see the work using factorization. Show
Enter 2 or more whole numbers separated by commas or spaces. The Greatest Common Factor Calculator solution also works as a solution for finding:
What is the Greatest Common Factor?The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6. Greatest Common Factor of 0Any non zero whole number times 0 equals 0 so it is true that every non zero whole number is a factor of 0. k × 0 = 0 so, 0 ÷ k = 0 for any whole number k. For example, 5 × 0 = 0 so it is true that 0 ÷ 5 = 0. In this example, 5 and 0 are factors of 0. GCF(5,0) = 5 and more generally GCF(k,0) = k for any whole number k. However, GCF(0, 0) is undefined. How to Find the Greatest Common Factor (GCF)There are several ways to find the greatest common factor of numbers. The most efficient method you use depends on how many numbers you have, how large they are and what you will do with the result. FactoringTo find the GCF by factoring, list out all of the factors of each number or find them with a Factors Calculator. The whole number factors are numbers that divide evenly into the number with zero remainder. Given the list of common factors for each number, the GCF is the largest number common to each list.
Prime FactorizationTo find the GCF by prime factorization, list out all of the prime factors of each number or find them with a Prime Factors Calculator. List the prime factors that are common to each of the original numbers. Include the highest number of occurrences of each prime factor that is common to each original number. Multiply these together to get the GCF. You will see that as numbers get larger the prime factorization method may be easier than straight factoring.
Euclid's AlgorithmWhat do you do if you want to find the GCF of more than two very large numbers such as 182664, 154875 and 137688? It's easy if you have a Factoring Calculator or a Prime Factorization Calculator or even the GCF calculator shown above. But if you need to do the factorization by hand it will be a lot of work. How to Find the GCF Using Euclid's Algorithm
For additional information see our Euclid's Algorithm Calculator.
References[1] Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 31st Edition. New York, NY: CRC Press, 2003 p. 101. [2] Weisstein, Eric W. "Greatest Common Divisor." From MathWorld--A Wolfram Web Resource. Help With Fractions: Finding the Greatest Common Factor. Wikipedia: Euclidean Algorithm. The gcf of 12 and 30 is the largest positive integer that divides the numbers 12 and 30 without a remainder. Spelled out, it is the greatest common factor of 12 and 30. Here you can find the gcf of 12 and 30, along with a total of three methods for computing it. This Greatest Common Factor Calculator is Really Cool! Click To TweetIn addition, we have a calculator you should check out. Not only can it determine the gcf of 12 and 30, but also that of three or more integers including twelve and thirty for example. Keep reading to learn everything about the gcf (12,30) and the terms related to it.What is the GCF of 12 and 30If you just want to know what is the greatest common factor of 12 and 30, it is 6. Usually, this is written as gcf(12,30) = 6The gcf of 12 and 30 can be obtained like this:
Taking the above into account you also know how to find all the common factors of 12 and 30, not just the greatest. In the next section we show you how to calculate the gcf of twelve and thirty by means of two more methods. How to find the GCF of 12 and 30The greatest common factor of 12 and 30 can be computed by using the least common multiple aka lcm of 12 and 30. This is the easiest approach: gcf (12,30) = = 6Alternatively, the gcf of 12 and 30 can be found using the prime factorization of 12 and 30:
In any case, the easiest way to compute the gcf of two numbers like 12 and 30 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 12,30. The calculation is conducted automatically. Similar searched terms on our site also include:
Use of GCF of 12 and 30What is the greatest common factor of 12 and 30 used for? Answer: It is helpful for reducing fractions like 12 / 30. Just divide the nominator as well as the denominator by the gcf (12,30) to reduce the fraction to lowest terms. . Properties of GCF of 12 and 30The most important properties of the gcf(12,30) are:
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 12 and 30 is 6. In common notation: gcf (12,30) = 6. If you have been searching for gcf 12 and 30 or gcf 12 30 then you have come to the correct page, too. The same is the true if you typed gcf for 12 and 30 in your favorite search engine. Note that you can find the greatest common factor of many integer pairs including twelve / thirty by using the search form in the sidebar of this page. Questions and comments related to the gcf of 12 and 30 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 12 and 30 has been useful to you, and make sure to bookmark our site. Thanks for your visit. |