What are the divisors of 2815?

1, 5, 563, 2815

There is a total of 4 positive divisors.
The sum of these divisors is 3384.
The arithmetic mean is 846.

4 odd divisors

1, 5, 563, 2815

How to compute the divisors of 2815?

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 2815 by each of the numbers from 1 to 2815 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)

2815 / 1 = 2815 (the remainder is 0, so 1 is a divisor of 2815)
2815 / 2 = 1407.5 (the remainder is 1, so 2 is not a divisor of 2815)
2815 / 3 = 938.33333333333 (the remainder is 1, so 3 is not a divisor of 2815)
...
2815 / 2814 = 1.000355366027 (the remainder is 1, so 2814 is not a divisor of 2815)
2815 / 2815 = 1 (the remainder is 0, so 2815 is a divisor of 2815)

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 2815 (i.e. 53.056573579529). 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 $\frac{N}{d} = D$ )

2815 / 1 = 2815 (the remainder is 0, so 1 and 2815 are divisors of 2815)
2815 / 2 = 1407.5 (the remainder is 1, so 2 is not a divisor of 2815)
2815 / 3 = 938.33333333333 (the remainder is 1, so 3 is not a divisor of 2815)
...
2815 / 52 = 54.134615384615 (the remainder is 7, so 52 is not a divisor of 2815)
2815 / 53 = 53.11320754717 (the remainder is 6, so 53 is not a divisor of 2815)