What are the divisors of 2256?

1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 94, 141, 188, 282, 376, 564, 752, 1128, 2256

There is a total of 20 positive divisors.
The sum of these divisors is 5952.
The arithmetic mean is 297.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 94, 188, 282, 376, 564, 752, 1128, 2256

4 odd divisors

1, 3, 47, 141

How to compute the divisors of 2256?

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 2256 by each of the numbers from 1 to 2256 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)

2256 / 1 = 2256 (the remainder is 0, so 1 is a divisor of 2256)
2256 / 2 = 1128 (the remainder is 0, so 2 is a divisor of 2256)
2256 / 3 = 752 (the remainder is 0, so 3 is a divisor of 2256)
...
2256 / 2255 = 1.00044345898 (the remainder is 1, so 2255 is not a divisor of 2256)
2256 / 2256 = 1 (the remainder is 0, so 2256 is a divisor of 2256)

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 2256 (i.e. 47.497368348152). 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 $\frac{N}{d} = D$ )

2256 / 1 = 2256 (the remainder is 0, so 1 and 2256 are divisors of 2256)
2256 / 2 = 1128 (the remainder is 0, so 2 and 1128 are divisors of 2256)
2256 / 3 = 752 (the remainder is 0, so 3 and 752 are divisors of 2256)
...
2256 / 46 = 49.04347826087 (the remainder is 2, so 46 is not a divisor of 2256)
2256 / 47 = 48 (the remainder is 0, so 47 and 48 are divisors of 2256)