What are the divisors of 818?

1, 2, 409, 818

There is a total of 4 positive divisors.
The sum of these divisors is 1230.
The arithmetic mean is 307.5.

2 even divisors

2, 818

2 odd divisors

1, 409

How to compute the divisors of 818?

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 818 by each of the numbers from 1 to 818 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)

818 / 1 = 818 (the remainder is 0, so 1 is a divisor of 818)
818 / 2 = 409 (the remainder is 0, so 2 is a divisor of 818)
818 / 3 = 272.66666666667 (the remainder is 2, so 3 is not a divisor of 818)
...
818 / 817 = 1.0012239902081 (the remainder is 1, so 817 is not a divisor of 818)
818 / 818 = 1 (the remainder is 0, so 818 is a divisor of 818)

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 818 (i.e. 28.60069929215). 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 $\frac{N}{d} = D$ )

818 / 1 = 818 (the remainder is 0, so 1 and 818 are divisors of 818)
818 / 2 = 409 (the remainder is 0, so 2 and 409 are divisors of 818)
818 / 3 = 272.66666666667 (the remainder is 2, so 3 is not a divisor of 818)
...
818 / 27 = 30.296296296296 (the remainder is 8, so 27 is not a divisor of 818)
818 / 28 = 29.214285714286 (the remainder is 6, so 28 is not a divisor of 818)