Given three numbers, our task is to find the largest number by which when given 3 numbers are divided leads to same remainder. It may be assumed that all given numbers are given in increasing order.
Input : a = 62, b = 132, c = 237 Output : 35 35 leads to same remainder 27 when divides 62, 132 and 237. Input : a = 74, b = 272, c = 584 Output : 6
The idea is based on the fact that if a number leaves same remainder with a, b and c, then it would divide their differences. Let us understand assuming that x is our result. Let a = x*d1 + r where r is the remainder when a is divided by x. Similarly we can write b = x*d2 + r and b = x*d3 + r. So the logic is here we first find differences of all three pairs and after that, we find greatest common divisor of differences to maximize result.
Below is the implementation of above idea.
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- Program to find remainder when large number is divided by r
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- Sum and product of k smallest and k largest composite numbers in the array
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