What are the divisors of 9056?

1, 2, 4, 8, 16, 32, 283, 566, 1132, 2264, 4528, 9056

There is a total of 12 positive divisors.
The sum of these divisors is 17892.
The arithmetic mean is 1491.

10 even divisors

2, 4, 8, 16, 32, 566, 1132, 2264, 4528, 9056

2 odd divisors

1, 283

How to compute the divisors of 9056?

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 9056 by each of the numbers from 1 to 9056 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)

9056 / 1 = 9056 (the remainder is 0, so 1 is a divisor of 9056)
9056 / 2 = 4528 (the remainder is 0, so 2 is a divisor of 9056)
9056 / 3 = 3018.6666666667 (the remainder is 2, so 3 is not a divisor of 9056)
...
9056 / 9055 = 1.0001104362231 (the remainder is 1, so 9055 is not a divisor of 9056)
9056 / 9056 = 1 (the remainder is 0, so 9056 is a divisor of 9056)

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 9056 (i.e. 95.163018026963). 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 $\frac{N}{d} = D$ )

9056 / 1 = 9056 (the remainder is 0, so 1 and 9056 are divisors of 9056)
9056 / 2 = 4528 (the remainder is 0, so 2 and 4528 are divisors of 9056)
9056 / 3 = 3018.6666666667 (the remainder is 2, so 3 is not a divisor of 9056)
...
9056 / 94 = 96.340425531915 (the remainder is 32, so 94 is not a divisor of 9056)
9056 / 95 = 95.326315789474 (the remainder is 31, so 95 is not a divisor of 9056)