What are the divisors of 9216?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2304, 3072, 4608, 9216

There is a total of 33 positive divisors.
The sum of these divisors is 26611.
The arithmetic mean is 806.39393939394.

30 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2304, 3072, 4608, 9216

3 odd divisors

1, 3, 9

How to compute the divisors of 9216?

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 9216 by each of the numbers from 1 to 9216 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)

9216 / 1 = 9216 (the remainder is 0, so 1 is a divisor of 9216)
9216 / 2 = 4608 (the remainder is 0, so 2 is a divisor of 9216)
9216 / 3 = 3072 (the remainder is 0, so 3 is a divisor of 9216)
...
9216 / 9215 = 1.0001085187195 (the remainder is 1, so 9215 is not a divisor of 9216)
9216 / 9216 = 1 (the remainder is 0, so 9216 is a divisor of 9216)

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 9216 (i.e. 96). 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 $\frac{N}{d} = D$ )

9216 / 1 = 9216 (the remainder is 0, so 1 and 9216 are divisors of 9216)
9216 / 2 = 4608 (the remainder is 0, so 2 and 4608 are divisors of 9216)
9216 / 3 = 3072 (the remainder is 0, so 3 and 3072 are divisors of 9216)
...
9216 / 95 = 97.010526315789 (the remainder is 1, so 95 is not a divisor of 9216)
9216 / 96 = 96 (the remainder is 0, so 96 and 96 are divisors of 9216)