How Do You Find The Greatest Common Divisor?
The greatest common divisor (GCD) is a math term that represents the largest integer that is divisible by each of two given integers. The following are true of the GCD: (1) there is no integer of greater value that divides into both integers and (2) the remainder is zero. There are two methods for finding the greatest common divisor. Perform a prime factorization on each integer. Find two factors of each integer, then continue to break the factors down until you’re left with only prime factors. The prime factors of 32 are 2*2*2*2*2, while they are 7*5 for 35. For more on prime factorization, see Resources below. Find common divisors of the two integers. Note any prime factor the two integers share. Multiply shared prime factors together. Through these basic math operations, you can find the GCD. For the above example, the GCD of 32 and 35 is 1. If the integers were 32 and 36, the GCD would be 4. Use the Euclidean Algorithm GCD(x,y) = GCD(y,r) where x and y are two integers and r is the
