The greatest common divisor (GCD), also called greatest common factor, is often used when trying to simplify fractions. Numbers can be broken down into factors, such as 2 x 3 = 6 where two and three are factors of six. The greatest common divisor is the largest factor shared between two numbers. When trying to find the GCD of very large numbers, use prime factorization to cut down on your work. Prime factorization works out which prime numbers, or numbers that can only be divided by 1 and themselves, multiply together to create the main number. Multiplying the common prime factors is a shortcut to the GCD for larger fractions.
Instructions
1. Find the greatest common divisor of the fraction 9/15 to simplify the fraction. Write out the factors of 9 which are the numbers that 9 can be divided by: 1, 3 and 9. Write out the factors of 15: 1, 3, 5 and 15. Circle the factors that the two numbers have in common: 1 and 3. Divide both numerator and denominator by the greatest common divisor of 3: (9/3)/(15/3) = 3/5.
2. Find the greatest common divisor of 42/108 to simplify the fraction. Write out the prime factors of the numbers only since the numbers are so large. Begin with 42: 1, 2, 3 and 7 (since 1 * 2 * 3 * 7 = 42). Find the prime factors for 108: 2, 2, 3, 3 and 3. Circle the common prime factors and multiply them together to find the greatest common divisor: 2 * 3 = 6. Divide each part of the fraction by 6: (42/6)/(108/6)= 7/18.
3. Find the greatest common divisor and simplify the fraction 45/75. Find the prime factors of 45: 3, 3 and 5. Find the prime factors of 75: 3, 5 and 5. Circle the common factors and multiply them together to get the greatest common divisor: 3 * 5 = 15. Divide each part of the fraction by 15 to simplify the fraction: (45/15) / (75/15) = 3/5.
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