What are the divisors of 9104?

1, 2, 4, 8, 16, 569, 1138, 2276, 4552, 9104

There is a total of 10 positive divisors.
The sum of these divisors is 17670.
The arithmetic mean is 1767.

8 even divisors

2, 4, 8, 16, 1138, 2276, 4552, 9104

2 odd divisors

1, 569

How to compute the divisors of 9104?

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 9104 by each of the numbers from 1 to 9104 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)

9104 / 1 = 9104 (the remainder is 0, so 1 is a divisor of 9104)
9104 / 2 = 4552 (the remainder is 0, so 2 is a divisor of 9104)
9104 / 3 = 3034.6666666667 (the remainder is 2, so 3 is not a divisor of 9104)
...
9104 / 9103 = 1.0001098538943 (the remainder is 1, so 9103 is not a divisor of 9104)
9104 / 9104 = 1 (the remainder is 0, so 9104 is a divisor of 9104)

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 9104 (i.e. 95.414883535013). 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 $\frac{N}{d} = D$ )

9104 / 1 = 9104 (the remainder is 0, so 1 and 9104 are divisors of 9104)
9104 / 2 = 4552 (the remainder is 0, so 2 and 4552 are divisors of 9104)
9104 / 3 = 3034.6666666667 (the remainder is 2, so 3 is not a divisor of 9104)
...
9104 / 94 = 96.851063829787 (the remainder is 80, so 94 is not a divisor of 9104)
9104 / 95 = 95.831578947368 (the remainder is 79, so 95 is not a divisor of 9104)