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This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
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Finding the greatest common factor (GCF)[1] of a number set can be easy, but there are several steps you'll need to follow to get there. In order to find the greatest common factor of two numbers, you'll need to factor out both of those numbers using your knowledge of timetables, then identify the largest number that appears in both sets of factors.
How to Do Greatest Common Factor (GCF)
- Factor out each number to the prime factors.
- Find the prime factors that each number has in common.
- Multiply the prime factors together to find the GCF.
Steps
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Find factors of the number. You don't have to know prime factorization to find the greatest common factor. Start by finding all the factors of the set you are comparing.[2] -
Compare the sets of factors until you find the biggest number that's in both sets.
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Identify any common prime factors.[4] Pick out any prime numbers between the set that are the same. There can be several common factors, one common factor, or none. -
Calculate: If there are no common factors then the greatest common factor is 1. If there's only one prime common factor, then that's your common factor. If there are multiple prime common factors, then multiply all the prime common factors together to get your greatest common factor[5] . -
To demonstrate this method, study this example.
Community Q&A
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QuestionWhat level of questions should I make for a test? Should I make the test easy, medium or hard?
Community AnswerIt depends upon your knowledge of your students. If you see that your students are very competitive and clever, you can make the test hard, so as to challenge their knowledge about the subject. If your students are beginners and have a lot to learn yet, making it easier will encourage them to keep learning more. -
QuestionWhat's the greatest common factor of 4x^3y, 8x^2y^3, xy^3z^5?
DonaganTop AnswererThe three terms are: 4x³y, 8x²y³, and xy³z^5. First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. The lowest x exponent is 1. The lowest y exponent is also 1. There is no z in two of the terms (so z is not a common factor). That means the greatest common factor among the three terms is 1xy (or xy). -
QuestionWhat is the use of prime numbers in our lives?
DonaganTop AnswererThe average person is never likely to use prime numbers. They do have certain applications within science and mathematics.
Video
Tips
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Did you know that the mathematician Euclid of the third century B.C.E. created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials?[6]Thanks
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A prime number is a number that can only be divided by one and itself.Thanks
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References
- ↑ https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-greatest-common-divisor/v/greatest-common-divisor
- ↑ https://www.mathsisfun.com/numbers/factors-all-tool.html
- ↑ https://mathworld.wolfram.com/PrimeNumber.html
- ↑ https://www.mathsisfun.com/prime-factorization.html
- ↑ https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-by-grouping
- ↑ https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm
About This Article
To find the greatest common factor of two or more numbers, make a list of all of the factors of each number. For example, for the number 10, the factors are 1, 2, 5, and 10, and for the number 21, the factors are 1, 3, 7, and 21. Then, compare the list of factors to find the largest number that the two have in common. For 10 and 21, the greatest common factor is 1. To learn more, like how to use prime numbers to find the greatest common factor, keep reading!
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