> For the complete documentation index, see [llms.txt](https://maksimdan.gitbook.io/interview-practice-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/507-perfect-number.md).

# 507 Perfect Number

We define the Perfect Number is a**positive**integer that is equal to the sum of all its**positive**divisors except itself.

Now, given an

**integer**

n, write a function that returns true when it is a perfect number and false when it is not.

**Example:**

```
Input:
 28

Output:
 True

Explanation:
 28 = 1 + 2 + 4 + 7 + 14
```

**Note:**The input number**n**will not exceed 100,000,000. (1e8)

Complexity: O(sqrt(n))

The Idea: We iterate through every possible number that can factor to n and sum up the results. There are a few optimizations here. First, a factor will not exceed sqrt(n), since sqrt(n)\*sqrt(n) == n.

```
Input:
 28

Sum:
 1

Explanation:
 28 = 1    +    2    +    4    +    7    +    14
      start
                ^------------------------------^
                          ^---------^
```

```python
class Solution(object):
    def checkPerfectNumber(self, num):
        """
        :type num: int
        :rtype: bool
        """
        if num == 1:
           return False

        acc_sum = 1
        max_fact = int(math.sqrt(abs(num)))
        for i in range(2, max_fact + 1):
            if num % i == 0:
                acc_sum += i + num / i

        return acc_sum == num
```


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