What are the divisors of 3594?

1, 2, 3, 6, 599, 1198, 1797, 3594

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

4 even divisors

2, 6, 1198, 3594

4 odd divisors

1, 3, 599, 1797

How to compute the divisors of 3594?

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 3594 by each of the numbers from 1 to 3594 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)

3594 / 1 = 3594 (the remainder is 0, so 1 is a divisor of 3594)
3594 / 2 = 1797 (the remainder is 0, so 2 is a divisor of 3594)
3594 / 3 = 1198 (the remainder is 0, so 3 is a divisor of 3594)
...
3594 / 3593 = 1.0002783189535 (the remainder is 1, so 3593 is not a divisor of 3594)
3594 / 3594 = 1 (the remainder is 0, so 3594 is a divisor of 3594)

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 3594 (i.e. 59.949979149287). 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 $\frac{N}{d} = D$ )

3594 / 1 = 3594 (the remainder is 0, so 1 and 3594 are divisors of 3594)
3594 / 2 = 1797 (the remainder is 0, so 2 and 1797 are divisors of 3594)
3594 / 3 = 1198 (the remainder is 0, so 3 and 1198 are divisors of 3594)
...
3594 / 58 = 61.965517241379 (the remainder is 56, so 58 is not a divisor of 3594)
3594 / 59 = 60.915254237288 (the remainder is 54, so 59 is not a divisor of 3594)