What are the divisors of 1599?

1, 3, 13, 39, 41, 123, 533, 1599

There is a total of 8 positive divisors.
The sum of these divisors is 2352.
The arithmetic mean is 294.

8 odd divisors

1, 3, 13, 39, 41, 123, 533, 1599

How to compute the divisors of 1599?

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 1599 by each of the numbers from 1 to 1599 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)

1599 / 1 = 1599 (the remainder is 0, so 1 is a divisor of 1599)
1599 / 2 = 799.5 (the remainder is 1, so 2 is not a divisor of 1599)
1599 / 3 = 533 (the remainder is 0, so 3 is a divisor of 1599)
...
1599 / 1598 = 1.0006257822278 (the remainder is 1, so 1598 is not a divisor of 1599)
1599 / 1599 = 1 (the remainder is 0, so 1599 is a divisor of 1599)

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 1599 (i.e. 39.987498046264). 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 $\frac{N}{d} = D$ )

1599 / 1 = 1599 (the remainder is 0, so 1 and 1599 are divisors of 1599)
1599 / 2 = 799.5 (the remainder is 1, so 2 is not a divisor of 1599)
1599 / 3 = 533 (the remainder is 0, so 3 and 533 are divisors of 1599)
...
1599 / 38 = 42.078947368421 (the remainder is 3, so 38 is not a divisor of 1599)
1599 / 39 = 41 (the remainder is 0, so 39 and 41 are divisors of 1599)