What are the divisors of 9080?

1, 2, 4, 5, 8, 10, 20, 40, 227, 454, 908, 1135, 1816, 2270, 4540, 9080

There is a total of 16 positive divisors.
The sum of these divisors is 20520.
The arithmetic mean is 1282.5.

12 even divisors

2, 4, 8, 10, 20, 40, 454, 908, 1816, 2270, 4540, 9080

4 odd divisors

1, 5, 227, 1135

How to compute the divisors of 9080?

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 9080 by each of the numbers from 1 to 9080 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)

9080 / 1 = 9080 (the remainder is 0, so 1 is a divisor of 9080)
9080 / 2 = 4540 (the remainder is 0, so 2 is a divisor of 9080)
9080 / 3 = 3026.6666666667 (the remainder is 2, so 3 is not a divisor of 9080)
...
9080 / 9079 = 1.000110144289 (the remainder is 1, so 9079 is not a divisor of 9080)
9080 / 9080 = 1 (the remainder is 0, so 9080 is a divisor of 9080)

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 9080 (i.e. 95.289033996573). 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 $\frac{N}{d} = D$ )

9080 / 1 = 9080 (the remainder is 0, so 1 and 9080 are divisors of 9080)
9080 / 2 = 4540 (the remainder is 0, so 2 and 4540 are divisors of 9080)
9080 / 3 = 3026.6666666667 (the remainder is 2, so 3 is not a divisor of 9080)
...
9080 / 94 = 96.595744680851 (the remainder is 56, so 94 is not a divisor of 9080)
9080 / 95 = 95.578947368421 (the remainder is 55, so 95 is not a divisor of 9080)