What are the divisors of 2056?

1, 2, 4, 8, 257, 514, 1028, 2056

There is a total of 8 positive divisors.
The sum of these divisors is 3870.
The arithmetic mean is 483.75.

6 even divisors

2, 4, 8, 514, 1028, 2056

2 odd divisors

1, 257

How to compute the divisors of 2056?

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 2056 by each of the numbers from 1 to 2056 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)

2056 / 1 = 2056 (the remainder is 0, so 1 is a divisor of 2056)
2056 / 2 = 1028 (the remainder is 0, so 2 is a divisor of 2056)
2056 / 3 = 685.33333333333 (the remainder is 1, so 3 is not a divisor of 2056)
...
2056 / 2055 = 1.0004866180049 (the remainder is 1, so 2055 is not a divisor of 2056)
2056 / 2056 = 1 (the remainder is 0, so 2056 is a divisor of 2056)

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 2056 (i.e. 45.343136195019). 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 $\frac{N}{d} = D$ )

2056 / 1 = 2056 (the remainder is 0, so 1 and 2056 are divisors of 2056)
2056 / 2 = 1028 (the remainder is 0, so 2 and 1028 are divisors of 2056)
2056 / 3 = 685.33333333333 (the remainder is 1, so 3 is not a divisor of 2056)
...
2056 / 44 = 46.727272727273 (the remainder is 32, so 44 is not a divisor of 2056)
2056 / 45 = 45.688888888889 (the remainder is 31, so 45 is not a divisor of 2056)