What are the divisors of 9176?

1, 2, 4, 8, 31, 37, 62, 74, 124, 148, 248, 296, 1147, 2294, 4588, 9176

There is a total of 16 positive divisors.
The sum of these divisors is 18240.
The arithmetic mean is 1140.

12 even divisors

2, 4, 8, 62, 74, 124, 148, 248, 296, 2294, 4588, 9176

4 odd divisors

1, 31, 37, 1147

How to compute the divisors of 9176?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9176 by each of the numbers from 1 to 9176 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9176 / 1 = 9176 (the remainder is 0, so 1 is a divisor of 9176)
9176 / 2 = 4588 (the remainder is 0, so 2 is a divisor of 9176)
9176 / 3 = 3058.6666666667 (the remainder is 2, so 3 is not a divisor of 9176)
...
9176 / 9175 = 1.0001089918256 (the remainder is 1, so 9175 is not a divisor of 9176)
9176 / 9176 = 1 (the remainder is 0, so 9176 is a divisor of 9176)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9176 (i.e. 95.791440118624). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9176 / 1 = 9176 (the remainder is 0, so 1 and 9176 are divisors of 9176)
9176 / 2 = 4588 (the remainder is 0, so 2 and 4588 are divisors of 9176)
9176 / 3 = 3058.6666666667 (the remainder is 2, so 3 is not a divisor of 9176)
...
9176 / 94 = 97.617021276596 (the remainder is 58, so 94 is not a divisor of 9176)
9176 / 95 = 96.589473684211 (the remainder is 56, so 95 is not a divisor of 9176)