What are the divisors of 597?

1, 3, 199, 597

There is a total of 4 positive divisors.
The sum of these divisors is 800.
The arithmetic mean is 200.

4 odd divisors

1, 3, 199, 597

How to compute the divisors of 597?

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 597 by each of the numbers from 1 to 597 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)

597 / 1 = 597 (the remainder is 0, so 1 is a divisor of 597)
597 / 2 = 298.5 (the remainder is 1, so 2 is not a divisor of 597)
597 / 3 = 199 (the remainder is 0, so 3 is a divisor of 597)
...
597 / 596 = 1.001677852349 (the remainder is 1, so 596 is not a divisor of 597)
597 / 597 = 1 (the remainder is 0, so 597 is a divisor of 597)

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 597 (i.e. 24.433583445741). 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 $\frac{N}{d} = D$ )

597 / 1 = 597 (the remainder is 0, so 1 and 597 are divisors of 597)
597 / 2 = 298.5 (the remainder is 1, so 2 is not a divisor of 597)
597 / 3 = 199 (the remainder is 0, so 3 and 199 are divisors of 597)
...
597 / 23 = 25.95652173913 (the remainder is 22, so 23 is not a divisor of 597)
597 / 24 = 24.875 (the remainder is 21, so 24 is not a divisor of 597)