What are the divisors of 5856?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 61, 96, 122, 183, 244, 366, 488, 732, 976, 1464, 1952, 2928, 5856

There is a total of 24 positive divisors.
The sum of these divisors is 15624.
The arithmetic mean is 651.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 96, 122, 244, 366, 488, 732, 976, 1464, 1952, 2928, 5856

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 5856?

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 5856 by each of the numbers from 1 to 5856 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)

5856 / 1 = 5856 (the remainder is 0, so 1 is a divisor of 5856)
5856 / 2 = 2928 (the remainder is 0, so 2 is a divisor of 5856)
5856 / 3 = 1952 (the remainder is 0, so 3 is a divisor of 5856)
...
5856 / 5855 = 1.000170794193 (the remainder is 1, so 5855 is not a divisor of 5856)
5856 / 5856 = 1 (the remainder is 0, so 5856 is a divisor of 5856)

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 5856 (i.e. 76.524505878836). 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 $\frac{N}{d} = D$ )

5856 / 1 = 5856 (the remainder is 0, so 1 and 5856 are divisors of 5856)
5856 / 2 = 2928 (the remainder is 0, so 2 and 2928 are divisors of 5856)
5856 / 3 = 1952 (the remainder is 0, so 3 and 1952 are divisors of 5856)
...
5856 / 75 = 78.08 (the remainder is 6, so 75 is not a divisor of 5856)
5856 / 76 = 77.052631578947 (the remainder is 4, so 76 is not a divisor of 5856)