What are the divisors of 599?

1, 599

There is a total of 2 positive divisors.
The sum of these divisors is 600.
The arithmetic mean is 300.

2 odd divisors

1, 599

How to compute the divisors of 599?

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 599 by each of the numbers from 1 to 599 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)

599 / 1 = 599 (the remainder is 0, so 1 is a divisor of 599)
599 / 2 = 299.5 (the remainder is 1, so 2 is not a divisor of 599)
599 / 3 = 199.66666666667 (the remainder is 2, so 3 is not a divisor of 599)
...
599 / 598 = 1.0016722408027 (the remainder is 1, so 598 is not a divisor of 599)
599 / 599 = 1 (the remainder is 0, so 599 is a divisor of 599)

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 599 (i.e. 24.474476501041). 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 $\frac{N}{d} = D$ )

599 / 1 = 599 (the remainder is 0, so 1 and 599 are divisors of 599)
599 / 2 = 299.5 (the remainder is 1, so 2 is not a divisor of 599)
599 / 3 = 199.66666666667 (the remainder is 2, so 3 is not a divisor of 599)
...
599 / 23 = 26.04347826087 (the remainder is 1, so 23 is not a divisor of 599)
599 / 24 = 24.958333333333 (the remainder is 23, so 24 is not a divisor of 599)