What are the divisors of 9184?

1, 2, 4, 7, 8, 14, 16, 28, 32, 41, 56, 82, 112, 164, 224, 287, 328, 574, 656, 1148, 1312, 2296, 4592, 9184

There is a total of 24 positive divisors.
The sum of these divisors is 21168.
The arithmetic mean is 882.

20 even divisors

2, 4, 8, 14, 16, 28, 32, 56, 82, 112, 164, 224, 328, 574, 656, 1148, 1312, 2296, 4592, 9184

4 odd divisors

1, 7, 41, 287

How to compute the divisors of 9184?

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 9184 by each of the numbers from 1 to 9184 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)

9184 / 1 = 9184 (the remainder is 0, so 1 is a divisor of 9184)
9184 / 2 = 4592 (the remainder is 0, so 2 is a divisor of 9184)
9184 / 3 = 3061.3333333333 (the remainder is 1, so 3 is not a divisor of 9184)
...
9184 / 9183 = 1.0001088968747 (the remainder is 1, so 9183 is not a divisor of 9184)
9184 / 9184 = 1 (the remainder is 0, so 9184 is a divisor of 9184)

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 9184 (i.e. 95.833188405688). 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 $\frac{N}{d} = D$ )

9184 / 1 = 9184 (the remainder is 0, so 1 and 9184 are divisors of 9184)
9184 / 2 = 4592 (the remainder is 0, so 2 and 4592 are divisors of 9184)
9184 / 3 = 3061.3333333333 (the remainder is 1, so 3 is not a divisor of 9184)
...
9184 / 94 = 97.702127659574 (the remainder is 66, so 94 is not a divisor of 9184)
9184 / 95 = 96.673684210526 (the remainder is 64, so 95 is not a divisor of 9184)