GCD of elements in a given range

Given two numbers n and m. Find the biggest integer a(gcd), such that all integers n, n + 1, n + 2, ..., m are divisible by a.
Examples: 
 

Input : n = 1, m = 2
Output: 1
Explanation:
Here, series become 1, 2. So, the 
greatest no which divides both of 
them is 1.

Input : n = 475, m = 475
Output : 475
Explanation:
Here, series has only one term 475.
So, greatest no which divides 475 is 475.

 

Here, We have to examine only two cases: 
 

1. if a = b : the segment consists of a single number, hence the answer is a.
2. if a < b : we have gcd(n, n + 1, n?+ 2, ..., m) = gcd(gcd(n, n + 1), n + 2, ..., m) = gcd(1, n + 2, ..., n) = 1.

Output:

475

Time Complexity: O(1)

Auxiliary Space: O(1)