Given two positive integer a and b and a range [low, high]. The task is to find the gretest common divisor of a and b which lie in the given range. If no divisor exist in the range, print -1.
Input : a = 9, b = 27, low = 1, high = 5 Output : 3 3 is the highest number that lies in range [1, 5] and is common divisor of 9 and 27. Input : a = 9, b = 27, low = 10, high = 11 Output : -1
The idea is to find the Greatest Common Divisor GCD(a, b) of a and b. Now observe, divisor of GCD(a, b) is also the divisor of a and b. So, we will iterate a loop i from 1 to sqrt(GCD(a, b)) and check if i divides GCD(a, b). Also, observe if i is divisor of GCD(a, b) then GCD(a, b)/i will also be divisor. So, for each iteration, if i divides GCD(a, b), we will find maximimum of i and GCD(a, b)/i if they lie in the range.
Below is the implementation of this approach:
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- Find a range of composite numbers of given length
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- Find the number of divisors of all numbers in the range [1, n]
- Count the number of intervals in which a given value lies
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- Find the number in a range having maximum product of the digits
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