What are the divisors of 9136?

1, 2, 4, 8, 16, 571, 1142, 2284, 4568, 9136

There is a total of 10 positive divisors.
The sum of these divisors is 17732.
The arithmetic mean is 1773.2.

8 even divisors

2, 4, 8, 16, 1142, 2284, 4568, 9136

2 odd divisors

1, 571

How to compute the divisors of 9136?

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 9136 by each of the numbers from 1 to 9136 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)

9136 / 1 = 9136 (the remainder is 0, so 1 is a divisor of 9136)
9136 / 2 = 4568 (the remainder is 0, so 2 is a divisor of 9136)
9136 / 3 = 3045.3333333333 (the remainder is 1, so 3 is not a divisor of 9136)
...
9136 / 9135 = 1.000109469075 (the remainder is 1, so 9135 is not a divisor of 9136)
9136 / 9136 = 1 (the remainder is 0, so 9136 is a divisor of 9136)

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 9136 (i.e. 95.582425162788). 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 $\frac{N}{d} = D$ )

9136 / 1 = 9136 (the remainder is 0, so 1 and 9136 are divisors of 9136)
9136 / 2 = 4568 (the remainder is 0, so 2 and 4568 are divisors of 9136)
9136 / 3 = 3045.3333333333 (the remainder is 1, so 3 is not a divisor of 9136)
...
9136 / 94 = 97.191489361702 (the remainder is 18, so 94 is not a divisor of 9136)
9136 / 95 = 96.168421052632 (the remainder is 16, so 95 is not a divisor of 9136)