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Self -Check Question The greatest common divisor (ged) of two numbers is the largest integer that divides both numbers. For example, the ged of 20,

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Self -Check Question The greatest common divisor (ged) of two numbers is the largest integer that divides both numbers. For example, the ged of 20, 15 is 5; the ged of 36, 24 is 12; the ged of 36, 18 is 18. The mathematician Euclid devised an algorithm for finding the great- est common divisor of two integers, m and n, based on the following definition. Definition of ged(m, n) for m>n ged(m, n)-n if n is a divisor of m gcd(m, n) = gcd(n, tn % n) if n isn't a divisor of m This definition states that ged(m, n) is n if n divides m. This is correct because no number larger than n can divide n. Otherwise, the definition states that gcd(m, n) is the same as gcd(n, m % n), where m % n is the integer remainder of m divided by n. Therefore, gcd(20, 15) is the same as ged(15, 5), or 5, because 5 divides 15. This recursive definition leads naturally to a recursive algorithm. Recursive gcd method (in RecursiveMethods.java). pre: m> 0 and n>0 @param m The Targer number Oparam n The smaTler number @return Greatest common divisor of m and n public static double gcd(int m, int n) f if (m % n-0) else if (m

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