What are the divisors of 5815?

1, 5, 1163, 5815

There is a total of 4 positive divisors.
The sum of these divisors is 6984.
The arithmetic mean is 1746.

4 odd divisors

1, 5, 1163, 5815

How to compute the divisors of 5815?

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 5815 by each of the numbers from 1 to 5815 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)

5815 / 1 = 5815 (the remainder is 0, so 1 is a divisor of 5815)
5815 / 2 = 2907.5 (the remainder is 1, so 2 is not a divisor of 5815)
5815 / 3 = 1938.3333333333 (the remainder is 1, so 3 is not a divisor of 5815)
...
5815 / 5814 = 1.000171998624 (the remainder is 1, so 5814 is not a divisor of 5815)
5815 / 5815 = 1 (the remainder is 0, so 5815 is a divisor of 5815)

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 5815 (i.e. 76.256147293185). 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 $\frac{N}{d} = D$ )

5815 / 1 = 5815 (the remainder is 0, so 1 and 5815 are divisors of 5815)
5815 / 2 = 2907.5 (the remainder is 1, so 2 is not a divisor of 5815)
5815 / 3 = 1938.3333333333 (the remainder is 1, so 3 is not a divisor of 5815)
...
5815 / 75 = 77.533333333333 (the remainder is 40, so 75 is not a divisor of 5815)
5815 / 76 = 76.513157894737 (the remainder is 39, so 76 is not a divisor of 5815)