What are the divisors of 809?

1, 809

There is a total of 2 positive divisors.
The sum of these divisors is 810.
The arithmetic mean is 405.

2 odd divisors

1, 809

How to compute the divisors of 809?

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 809 by each of the numbers from 1 to 809 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)

809 / 1 = 809 (the remainder is 0, so 1 is a divisor of 809)
809 / 2 = 404.5 (the remainder is 1, so 2 is not a divisor of 809)
809 / 3 = 269.66666666667 (the remainder is 2, so 3 is not a divisor of 809)
...
809 / 808 = 1.0012376237624 (the remainder is 1, so 808 is not a divisor of 809)
809 / 809 = 1 (the remainder is 0, so 809 is a divisor of 809)

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 809 (i.e. 28.442925306656). 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 $\frac{N}{d} = D$ )

809 / 1 = 809 (the remainder is 0, so 1 and 809 are divisors of 809)
809 / 2 = 404.5 (the remainder is 1, so 2 is not a divisor of 809)
809 / 3 = 269.66666666667 (the remainder is 2, so 3 is not a divisor of 809)
...
809 / 27 = 29.962962962963 (the remainder is 26, so 27 is not a divisor of 809)
809 / 28 = 28.892857142857 (the remainder is 25, so 28 is not a divisor of 809)