What are the divisors of 817?

1, 19, 43, 817

There is a total of 4 positive divisors.
The sum of these divisors is 880.
The arithmetic mean is 220.

4 odd divisors

1, 19, 43, 817

How to compute the divisors of 817?

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 817 by each of the numbers from 1 to 817 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)

817 / 1 = 817 (the remainder is 0, so 1 is a divisor of 817)
817 / 2 = 408.5 (the remainder is 1, so 2 is not a divisor of 817)
817 / 3 = 272.33333333333 (the remainder is 1, so 3 is not a divisor of 817)
...
817 / 816 = 1.0012254901961 (the remainder is 1, so 816 is not a divisor of 817)
817 / 817 = 1 (the remainder is 0, so 817 is a divisor of 817)

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 817 (i.e. 28.583211855913). 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 $\frac{N}{d} = D$ )

817 / 1 = 817 (the remainder is 0, so 1 and 817 are divisors of 817)
817 / 2 = 408.5 (the remainder is 1, so 2 is not a divisor of 817)
817 / 3 = 272.33333333333 (the remainder is 1, so 3 is not a divisor of 817)
...
817 / 27 = 30.259259259259 (the remainder is 7, so 27 is not a divisor of 817)
817 / 28 = 29.178571428571 (the remainder is 5, so 28 is not a divisor of 817)