What are the divisors of 9152?

1, 2, 4, 8, 11, 13, 16, 22, 26, 32, 44, 52, 64, 88, 104, 143, 176, 208, 286, 352, 416, 572, 704, 832, 1144, 2288, 4576, 9152

There is a total of 28 positive divisors.
The sum of these divisors is 21336.
The arithmetic mean is 762.

24 even divisors

2, 4, 8, 16, 22, 26, 32, 44, 52, 64, 88, 104, 176, 208, 286, 352, 416, 572, 704, 832, 1144, 2288, 4576, 9152

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 9152?

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 9152 by each of the numbers from 1 to 9152 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)

9152 / 1 = 9152 (the remainder is 0, so 1 is a divisor of 9152)
9152 / 2 = 4576 (the remainder is 0, so 2 is a divisor of 9152)
9152 / 3 = 3050.6666666667 (the remainder is 2, so 3 is not a divisor of 9152)
...
9152 / 9151 = 1.0001092776746 (the remainder is 1, so 9151 is not a divisor of 9152)
9152 / 9152 = 1 (the remainder is 0, so 9152 is a divisor of 9152)

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 9152 (i.e. 95.666085944811). 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 $\frac{N}{d} = D$ )

9152 / 1 = 9152 (the remainder is 0, so 1 and 9152 are divisors of 9152)
9152 / 2 = 4576 (the remainder is 0, so 2 and 4576 are divisors of 9152)
9152 / 3 = 3050.6666666667 (the remainder is 2, so 3 is not a divisor of 9152)
...
9152 / 94 = 97.36170212766 (the remainder is 34, so 94 is not a divisor of 9152)
9152 / 95 = 96.336842105263 (the remainder is 32, so 95 is not a divisor of 9152)