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# Consecutive Numbers Sum

Given a positive integer `N`, how many ways can we write it as a sum of consecutive positive integers?

**Example 1:**

```
Input: 5
Output: 2
Explanation: 5 = 5 = 2 + 3
```

**Example 2:**

```
Input: 9
Output: 3
Explanation: 9 = 9 = 4 + 5 = 2 + 3 + 4
```

**Example 3:**

```
Input: 15
Output: 4
Explanation: 15 = 15 = 8 + 7 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5
```

**Note:** `1 <= N <= 10 ^ 9`.

```java
class Solution {
    public int consecutiveNumbersSum(int N) {
        // for K consecutive numbers
        // N= x+ (x+1)+(x+2) ... + (x+k-1)
        // N= Kx + K*(K-1)/2
        int count = 1;
        for (int k = 2; k * k <= 2 * N; k++)
            if ((N - (k * (k - 1)) / 2) % k == 0)
                count++;
        return count;
    }
}
```