What are the divisors of 808?

1, 2, 4, 8, 101, 202, 404, 808

There is a total of 8 positive divisors.
The sum of these divisors is 1530.
The arithmetic mean is 191.25.

6 even divisors

2, 4, 8, 202, 404, 808

2 odd divisors

1, 101

How to compute the divisors of 808?

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 808 by each of the numbers from 1 to 808 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)

808 / 1 = 808 (the remainder is 0, so 1 is a divisor of 808)
808 / 2 = 404 (the remainder is 0, so 2 is a divisor of 808)
808 / 3 = 269.33333333333 (the remainder is 1, so 3 is not a divisor of 808)
...
808 / 807 = 1.001239157373 (the remainder is 1, so 807 is not a divisor of 808)
808 / 808 = 1 (the remainder is 0, so 808 is a divisor of 808)

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 808 (i.e. 28.425340807104). 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 $\frac{N}{d} = D$ )

808 / 1 = 808 (the remainder is 0, so 1 and 808 are divisors of 808)
808 / 2 = 404 (the remainder is 0, so 2 and 404 are divisors of 808)
808 / 3 = 269.33333333333 (the remainder is 1, so 3 is not a divisor of 808)
...
808 / 27 = 29.925925925926 (the remainder is 25, so 27 is not a divisor of 808)
808 / 28 = 28.857142857143 (the remainder is 24, so 28 is not a divisor of 808)