Given an integer n. Check whether the number is refactorable or not. A refactorable number is an integer n that is divisible by count of all it’s divisors.
Input: n = 8 Output: yes Explanation: 8 has 4 divisors: 1, 2, 4, 8 Since 8 is divisible by 4 therefore 8 is refactorable number. Input : n = 4 Output: no
This solution is pretty straightforward. The idea is to iterate from 1 to sqrt(n) and count all the divisors of a number. After that we just need to check whether the number n is divisible by it’s total count or not.
Output: yes no
Time complexity: O(sqrt(n))
Auxiliary space: O(1)
Facts about refactorable number
- There is no refactorable number which is perfect.
- There is no three consecutive integers can all be refactorable.
- Refactorable number have natural density zero.
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