What are the divisors of 4596?

1, 2, 3, 4, 6, 12, 383, 766, 1149, 1532, 2298, 4596

There is a total of 12 positive divisors.
The sum of these divisors is 10752.
The arithmetic mean is 896.

8 even divisors

2, 4, 6, 12, 766, 1532, 2298, 4596

4 odd divisors

1, 3, 383, 1149

How to compute the divisors of 4596?

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 4596 by each of the numbers from 1 to 4596 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)

4596 / 1 = 4596 (the remainder is 0, so 1 is a divisor of 4596)
4596 / 2 = 2298 (the remainder is 0, so 2 is a divisor of 4596)
4596 / 3 = 1532 (the remainder is 0, so 3 is a divisor of 4596)
...
4596 / 4595 = 1.0002176278564 (the remainder is 1, so 4595 is not a divisor of 4596)
4596 / 4596 = 1 (the remainder is 0, so 4596 is a divisor of 4596)

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 4596 (i.e. 67.793805026713). 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 $\frac{N}{d} = D$ )

4596 / 1 = 4596 (the remainder is 0, so 1 and 4596 are divisors of 4596)
4596 / 2 = 2298 (the remainder is 0, so 2 and 2298 are divisors of 4596)
4596 / 3 = 1532 (the remainder is 0, so 3 and 1532 are divisors of 4596)
...
4596 / 66 = 69.636363636364 (the remainder is 42, so 66 is not a divisor of 4596)
4596 / 67 = 68.597014925373 (the remainder is 40, so 67 is not a divisor of 4596)