What are the divisors of 594?

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 198, 297, 594

There is a total of 16 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 90.

8 even divisors

2, 6, 18, 22, 54, 66, 198, 594

8 odd divisors

1, 3, 9, 11, 27, 33, 99, 297

How to compute the divisors of 594?

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 594 by each of the numbers from 1 to 594 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)

594 / 1 = 594 (the remainder is 0, so 1 is a divisor of 594)
594 / 2 = 297 (the remainder is 0, so 2 is a divisor of 594)
594 / 3 = 198 (the remainder is 0, so 3 is a divisor of 594)
...
594 / 593 = 1.0016863406408 (the remainder is 1, so 593 is not a divisor of 594)
594 / 594 = 1 (the remainder is 0, so 594 is a divisor of 594)

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 594 (i.e. 24.372115213908). 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 $\frac{N}{d} = D$ )

594 / 1 = 594 (the remainder is 0, so 1 and 594 are divisors of 594)
594 / 2 = 297 (the remainder is 0, so 2 and 297 are divisors of 594)
594 / 3 = 198 (the remainder is 0, so 3 and 198 are divisors of 594)
...
594 / 23 = 25.826086956522 (the remainder is 19, so 23 is not a divisor of 594)
594 / 24 = 24.75 (the remainder is 18, so 24 is not a divisor of 594)