What are the divisors of 323?

1, 17, 19, 323

There is a total of 4 positive divisors.
The sum of these divisors is 360.
The arithmetic mean is 90.

4 odd divisors

1, 17, 19, 323

How to compute the divisors of 323?

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 323 by each of the numbers from 1 to 323 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)

323 / 1 = 323 (the remainder is 0, so 1 is a divisor of 323)
323 / 2 = 161.5 (the remainder is 1, so 2 is not a divisor of 323)
323 / 3 = 107.66666666667 (the remainder is 2, so 3 is not a divisor of 323)
...
323 / 322 = 1.0031055900621 (the remainder is 1, so 322 is not a divisor of 323)
323 / 323 = 1 (the remainder is 0, so 323 is a divisor of 323)

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 323 (i.e. 17.972200755611). 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 $\frac{N}{d} = D$ )

323 / 1 = 323 (the remainder is 0, so 1 and 323 are divisors of 323)
323 / 2 = 161.5 (the remainder is 1, so 2 is not a divisor of 323)
323 / 3 = 107.66666666667 (the remainder is 2, so 3 is not a divisor of 323)
...
323 / 16 = 20.1875 (the remainder is 3, so 16 is not a divisor of 323)
323 / 17 = 19 (the remainder is 0, so 17 and 19 are divisors of 323)