What are the divisors of 8032?

1, 2, 4, 8, 16, 32, 251, 502, 1004, 2008, 4016, 8032

There is a total of 12 positive divisors.
The sum of these divisors is 15876.
The arithmetic mean is 1323.

10 even divisors

2, 4, 8, 16, 32, 502, 1004, 2008, 4016, 8032

2 odd divisors

1, 251

How to compute the divisors of 8032?

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 8032 by each of the numbers from 1 to 8032 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)

8032 / 1 = 8032 (the remainder is 0, so 1 is a divisor of 8032)
8032 / 2 = 4016 (the remainder is 0, so 2 is a divisor of 8032)
8032 / 3 = 2677.3333333333 (the remainder is 1, so 3 is not a divisor of 8032)
...
8032 / 8031 = 1.0001245174947 (the remainder is 1, so 8031 is not a divisor of 8032)
8032 / 8032 = 1 (the remainder is 0, so 8032 is a divisor of 8032)

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 8032 (i.e. 89.621426009632). 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 $\frac{N}{d} = D$ )

8032 / 1 = 8032 (the remainder is 0, so 1 and 8032 are divisors of 8032)
8032 / 2 = 4016 (the remainder is 0, so 2 and 4016 are divisors of 8032)
8032 / 3 = 2677.3333333333 (the remainder is 1, so 3 is not a divisor of 8032)
...
8032 / 88 = 91.272727272727 (the remainder is 24, so 88 is not a divisor of 8032)
8032 / 89 = 90.247191011236 (the remainder is 22, so 89 is not a divisor of 8032)