What are the divisors of 9016?

1, 2, 4, 7, 8, 14, 23, 28, 46, 49, 56, 92, 98, 161, 184, 196, 322, 392, 644, 1127, 1288, 2254, 4508, 9016

There is a total of 24 positive divisors.
The sum of these divisors is 20520.
The arithmetic mean is 855.

18 even divisors

2, 4, 8, 14, 28, 46, 56, 92, 98, 184, 196, 322, 392, 644, 1288, 2254, 4508, 9016

6 odd divisors

1, 7, 23, 49, 161, 1127

How to compute the divisors of 9016?

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 9016 by each of the numbers from 1 to 9016 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)

9016 / 1 = 9016 (the remainder is 0, so 1 is a divisor of 9016)
9016 / 2 = 4508 (the remainder is 0, so 2 is a divisor of 9016)
9016 / 3 = 3005.3333333333 (the remainder is 1, so 3 is not a divisor of 9016)
...
9016 / 9015 = 1.0001109262341 (the remainder is 1, so 9015 is not a divisor of 9016)
9016 / 9016 = 1 (the remainder is 0, so 9016 is a divisor of 9016)

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 9016 (i.e. 94.952619763754). 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 $\frac{N}{d} = D$ )

9016 / 1 = 9016 (the remainder is 0, so 1 and 9016 are divisors of 9016)
9016 / 2 = 4508 (the remainder is 0, so 2 and 4508 are divisors of 9016)
9016 / 3 = 3005.3333333333 (the remainder is 1, so 3 is not a divisor of 9016)
...
9016 / 93 = 96.94623655914 (the remainder is 88, so 93 is not a divisor of 9016)
9016 / 94 = 95.914893617021 (the remainder is 86, so 94 is not a divisor of 9016)