Given Input numbers are 15, 12, 10 Show To find the GCF of numbers using factoring list out all the factors of each number Factors of 15 List of positive integer factors of 15 that divides 15 without a remainder. 1, 3, 5, 15 Factors of 12 List of positive integer factors of 12 that divides 12 without a remainder. 1, 2, 3, 4, 6, 12 Factors of 10 List of positive integer factors of 10 that divides 10 without a remainder. 1, 2, 5, 10 Greatest Common Factor We found the factors of 15, 12, 10 . The biggest common factor number is the GCF number. Therefore, GCF of numbers 15, 12, 10 is 1
What is the GCF of 12 and 15? GCF is the abbreviation for Greatest Common Factor. Therefore, the GCF of 12 and 15 is the same as the Greatest Common Factor of 12 and 15. The GCF of 12 and 15 is the largest positive integer by which both 12 and 15 can be divided. Furthermore, both 12 and 15 have a set of factors and the GCF is the greatest factor that 12 and 15 have in common.Compare factors to get GCF of 12 and 15 Per definition above, to find the GCF of 12 and 15, you can compare the factors of 12 with the factors of 15 to see which factor is the greatest. When we did that, we found that the Greatest Common Factor (GCF) of 12 and 15 is 3. Use LCM to get GCF of 12 and 15 The Least Common Multiple (LCM) of 12 and 15 is 60. You can find the GCF of 12 and 15 by dividing the product of 12 and 15 by the LCM of 12 and 15. Here is the formula and math:
Use computer spreadsheet to get GCF of 12 and 15 If you have a computer, you can also use a spreadsheet in Excel or Numbers to calculate the GCF of 12 and 15. You want to type =gcf(12, 15) into a cell to get the answer. gcf(12, 15) = 3 Use the GCF of 12 and 15 to simplify a fraction The GCF of 12 and 15 can be used for many things. You can, for example, simplify a fraction by dividing the numerator and denominator by the GCF like this: Use GCF of 12 and 15 to simplify a ratio Similarly, you can use the GCF of 12 and 15 to simplify a ratio by dividing each part of the ratio by the GCF like this: = 12 : 15 = (12 ÷ 3) : (15 ÷ 3) = 4 : 5 Use the GCF of 12 and 15 to find the LCM of 12 and 15 Since using the Least Common Multiple (LCM) is one of the ways to find the GCF of 12 and 15, you can use the GCF of 12 and 15 to find the LCM of 12 and 15. The LCM of 12 and 15 can, for example, be used to add and subtract fractions with denominators of 12 and 15. The LCM of 12 and 15 is the product of 12 and 15 divided by the GCF of 12 and 15. Here is the math:
That is all there is to it! We hope this page accomplished its goal of defining the GCF of 12 and 15 by showing you how to calculate the GCF, examples of its uses, and how it relates to LCM. GCF Calculator GCF of 12 and 16 Here is the next GCF on our list that we have calculated and explained for you. Copyright | Privacy Policy | Disclaimer | Contact
Calculate GCF, GCD and HCF of a set of two or more numbers and see the work using factorization. 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. |