What are the divisors of 9248?

1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 289, 544, 578, 1156, 2312, 4624, 9248

There is a total of 18 positive divisors.
The sum of these divisors is 19341.
The arithmetic mean is 1074.5.

15 even divisors

2, 4, 8, 16, 32, 34, 68, 136, 272, 544, 578, 1156, 2312, 4624, 9248

3 odd divisors

1, 17, 289

How to compute the divisors of 9248?

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 9248 by each of the numbers from 1 to 9248 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)

9248 / 1 = 9248 (the remainder is 0, so 1 is a divisor of 9248)
9248 / 2 = 4624 (the remainder is 0, so 2 is a divisor of 9248)
9248 / 3 = 3082.6666666667 (the remainder is 2, so 3 is not a divisor of 9248)
...
9248 / 9247 = 1.0001081431816 (the remainder is 1, so 9247 is not a divisor of 9248)
9248 / 9248 = 1 (the remainder is 0, so 9248 is a divisor of 9248)

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 9248 (i.e. 96.16652224137). 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 $\frac{N}{d} = D$ )

9248 / 1 = 9248 (the remainder is 0, so 1 and 9248 are divisors of 9248)
9248 / 2 = 4624 (the remainder is 0, so 2 and 4624 are divisors of 9248)
9248 / 3 = 3082.6666666667 (the remainder is 2, so 3 is not a divisor of 9248)
...
9248 / 95 = 97.347368421053 (the remainder is 33, so 95 is not a divisor of 9248)
9248 / 96 = 96.333333333333 (the remainder is 32, so 96 is not a divisor of 9248)