The greatest common divisor (gcd) of two positive integers is the largest integer that divides evenly into both of them. for example, the gcd (102, 68) = 34. we can efficiently compute the gcd using the following property, which holds for positive integers p and q: if p > q, the gcd of p and q is the same as the gcd of q and p % q. in euclid's algorithm, we start with two numbers x and y. if y is zero then greatest common divisor of both will be x, but if y is not zero then we assign the y to x and y becomes x%y. once again we check if y is zero, if yes then we have our greatest common divisor or gcd otherwise we keep continue like this until y becomes zero. since we are using modulo operator, the number is getting smaller and smaller at each iteration, so the x%y will eventually become zero. let' take an example of calculating gcd of 54 and 24 using euclid's algorithm. here x = 54 and y = 24, since y is not zero we move to the logical part and assign x y, which means x becomes 24 and y becomes 54%24 i. e. 6. since y is still not zero, we again apply the logic. this times x will become 6 and y will become 24%6 i. e. y = 0 bingo, y is now zero which means we have our answer and it's nothing but the value of x which is 6 (six). write a recursive java program to calculate the gcd by euclid's method.