What are the divisors of 5816?

1, 2, 4, 8, 727, 1454, 2908, 5816

There is a total of 8 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 1365.

6 even divisors

2, 4, 8, 1454, 2908, 5816

2 odd divisors

1, 727

How to compute the divisors of 5816?

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 5816 by each of the numbers from 1 to 5816 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)

5816 / 1 = 5816 (the remainder is 0, so 1 is a divisor of 5816)
5816 / 2 = 2908 (the remainder is 0, so 2 is a divisor of 5816)
5816 / 3 = 1938.6666666667 (the remainder is 2, so 3 is not a divisor of 5816)
...
5816 / 5815 = 1.0001719690456 (the remainder is 1, so 5815 is not a divisor of 5816)
5816 / 5816 = 1 (the remainder is 0, so 5816 is a divisor of 5816)

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 5816 (i.e. 76.26270385975). 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 $\frac{N}{d} = D$ )

5816 / 1 = 5816 (the remainder is 0, so 1 and 5816 are divisors of 5816)
5816 / 2 = 2908 (the remainder is 0, so 2 and 2908 are divisors of 5816)
5816 / 3 = 1938.6666666667 (the remainder is 2, so 3 is not a divisor of 5816)
...
5816 / 75 = 77.546666666667 (the remainder is 41, so 75 is not a divisor of 5816)
5816 / 76 = 76.526315789474 (the remainder is 40, so 76 is not a divisor of 5816)