What are the divisors of 813?

1, 3, 271, 813

There is a total of 4 positive divisors.
The sum of these divisors is 1088.
The arithmetic mean is 272.

4 odd divisors

1, 3, 271, 813

How to compute the divisors of 813?

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 813 by each of the numbers from 1 to 813 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)

813 / 1 = 813 (the remainder is 0, so 1 is a divisor of 813)
813 / 2 = 406.5 (the remainder is 1, so 2 is not a divisor of 813)
813 / 3 = 271 (the remainder is 0, so 3 is a divisor of 813)
...
813 / 812 = 1.0012315270936 (the remainder is 1, so 812 is not a divisor of 813)
813 / 813 = 1 (the remainder is 0, so 813 is a divisor of 813)

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 813 (i.e. 28.513154858767). 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 $\frac{N}{d} = D$ )

813 / 1 = 813 (the remainder is 0, so 1 and 813 are divisors of 813)
813 / 2 = 406.5 (the remainder is 1, so 2 is not a divisor of 813)
813 / 3 = 271 (the remainder is 0, so 3 and 271 are divisors of 813)
...
813 / 27 = 30.111111111111 (the remainder is 3, so 27 is not a divisor of 813)
813 / 28 = 29.035714285714 (the remainder is 1, so 28 is not a divisor of 813)