What are the divisors of 256?

1, 2, 4, 8, 16, 32, 64, 128, 256

There is a total of 9 positive divisors.
The sum of these divisors is 511.
The arithmetic mean is 56.777777777778.

8 even divisors

2, 4, 8, 16, 32, 64, 128, 256

1 odd divisors

How to compute the divisors of 256?

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 256 by each of the numbers from 1 to 256 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)

256 / 1 = 256 (the remainder is 0, so 1 is a divisor of 256)
256 / 2 = 128 (the remainder is 0, so 2 is a divisor of 256)
256 / 3 = 85.333333333333 (the remainder is 1, so 3 is not a divisor of 256)
...
256 / 255 = 1.0039215686275 (the remainder is 1, so 255 is not a divisor of 256)
256 / 256 = 1 (the remainder is 0, so 256 is a divisor of 256)

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 256 (i.e. 16). 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 $\frac{N}{d} = D$ )

256 / 1 = 256 (the remainder is 0, so 1 and 256 are divisors of 256)
256 / 2 = 128 (the remainder is 0, so 2 and 128 are divisors of 256)
256 / 3 = 85.333333333333 (the remainder is 1, so 3 is not a divisor of 256)
...
256 / 15 = 17.066666666667 (the remainder is 1, so 15 is not a divisor of 256)
256 / 16 = 16 (the remainder is 0, so 16 and 16 are divisors of 256)