What are the divisors of 9160?

1, 2, 4, 5, 8, 10, 20, 40, 229, 458, 916, 1145, 1832, 2290, 4580, 9160

There is a total of 16 positive divisors.
The sum of these divisors is 20700.
The arithmetic mean is 1293.75.

12 even divisors

2, 4, 8, 10, 20, 40, 458, 916, 1832, 2290, 4580, 9160

4 odd divisors

1, 5, 229, 1145

How to compute the divisors of 9160?

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 9160 by each of the numbers from 1 to 9160 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)

9160 / 1 = 9160 (the remainder is 0, so 1 is a divisor of 9160)
9160 / 2 = 4580 (the remainder is 0, so 2 is a divisor of 9160)
9160 / 3 = 3053.3333333333 (the remainder is 1, so 3 is not a divisor of 9160)
...
9160 / 9159 = 1.0001091822251 (the remainder is 1, so 9159 is not a divisor of 9160)
9160 / 9160 = 1 (the remainder is 0, so 9160 is a divisor of 9160)

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 9160 (i.e. 95.707888912043). 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 $\frac{N}{d} = D$ )

9160 / 1 = 9160 (the remainder is 0, so 1 and 9160 are divisors of 9160)
9160 / 2 = 4580 (the remainder is 0, so 2 and 4580 are divisors of 9160)
9160 / 3 = 3053.3333333333 (the remainder is 1, so 3 is not a divisor of 9160)
...
9160 / 94 = 97.446808510638 (the remainder is 42, so 94 is not a divisor of 9160)
9160 / 95 = 96.421052631579 (the remainder is 40, so 95 is not a divisor of 9160)