The greatest common factor of a set of numbers is the largest number that will divide into each number within the set evenly. One of the most-efficient methods of finding the greatest common factor is the process of prime factorization. A prime number is a number that can only be divided evenly by itself and the number 1. Prime factorization simplifies a value into the prime numbers that can be multiplied to create the total number. Finding the greatest common factor is a common part of simplifying fractions.
Instructions
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1
Write down the numbers from which you will extract the greatest common factor. For example, you might have the fraction 40/75.
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2
Break down each number into its prime factors. In this example, you would break 40 into 2 * 2 * 2 * 5. You also would break 75 into 3 * 3 * 5.
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Compare the prime factors and underline any common prime factors between the two numbers. In this case, 5 is the only common factor (and the greatest common factor). The largest shared prime factor between the two numbers is the greatest common factor.