What are the divisors of 4593?

1, 3, 1531, 4593

There is a total of 4 positive divisors.
The sum of these divisors is 6128.
The arithmetic mean is 1532.

4 odd divisors

1, 3, 1531, 4593

How to compute the divisors of 4593?

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 4593 by each of the numbers from 1 to 4593 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)

4593 / 1 = 4593 (the remainder is 0, so 1 is a divisor of 4593)
4593 / 2 = 2296.5 (the remainder is 1, so 2 is not a divisor of 4593)
4593 / 3 = 1531 (the remainder is 0, so 3 is a divisor of 4593)
...
4593 / 4592 = 1.0002177700348 (the remainder is 1, so 4592 is not a divisor of 4593)
4593 / 4593 = 1 (the remainder is 0, so 4593 is a divisor of 4593)

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 4593 (i.e. 67.77167549943). 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 $\frac{N}{d} = D$ )

4593 / 1 = 4593 (the remainder is 0, so 1 and 4593 are divisors of 4593)
4593 / 2 = 2296.5 (the remainder is 1, so 2 is not a divisor of 4593)
4593 / 3 = 1531 (the remainder is 0, so 3 and 1531 are divisors of 4593)
...
4593 / 66 = 69.590909090909 (the remainder is 39, so 66 is not a divisor of 4593)
4593 / 67 = 68.55223880597 (the remainder is 37, so 67 is not a divisor of 4593)