What are the divisors of 1856?

1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 232, 464, 928, 1856

There is a total of 14 positive divisors.
The sum of these divisors is 3810.
The arithmetic mean is 272.14285714286.

12 even divisors

2, 4, 8, 16, 32, 58, 64, 116, 232, 464, 928, 1856

2 odd divisors

1, 29

How to compute the divisors of 1856?

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 1856 by each of the numbers from 1 to 1856 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)

1856 / 1 = 1856 (the remainder is 0, so 1 is a divisor of 1856)
1856 / 2 = 928 (the remainder is 0, so 2 is a divisor of 1856)
1856 / 3 = 618.66666666667 (the remainder is 2, so 3 is not a divisor of 1856)
...
1856 / 1855 = 1.000539083558 (the remainder is 1, so 1855 is not a divisor of 1856)
1856 / 1856 = 1 (the remainder is 0, so 1856 is a divisor of 1856)

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 1856 (i.e. 43.081318457076). 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 $\frac{N}{d} = D$ )

1856 / 1 = 1856 (the remainder is 0, so 1 and 1856 are divisors of 1856)
1856 / 2 = 928 (the remainder is 0, so 2 and 928 are divisors of 1856)
1856 / 3 = 618.66666666667 (the remainder is 2, so 3 is not a divisor of 1856)
...
1856 / 42 = 44.190476190476 (the remainder is 8, so 42 is not a divisor of 1856)
1856 / 43 = 43.162790697674 (the remainder is 7, so 43 is not a divisor of 1856)