What are the divisors of 4584?

1, 2, 3, 4, 6, 8, 12, 24, 191, 382, 573, 764, 1146, 1528, 2292, 4584

There is a total of 16 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 720.

12 even divisors

2, 4, 6, 8, 12, 24, 382, 764, 1146, 1528, 2292, 4584

4 odd divisors

1, 3, 191, 573

How to compute the divisors of 4584?

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 4584 by each of the numbers from 1 to 4584 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)

4584 / 1 = 4584 (the remainder is 0, so 1 is a divisor of 4584)
4584 / 2 = 2292 (the remainder is 0, so 2 is a divisor of 4584)
4584 / 3 = 1528 (the remainder is 0, so 3 is a divisor of 4584)
...
4584 / 4583 = 1.0002181976871 (the remainder is 1, so 4583 is not a divisor of 4584)
4584 / 4584 = 1 (the remainder is 0, so 4584 is a divisor of 4584)

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 4584 (i.e. 67.705243519243). 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 $\frac{N}{d} = D$ )

4584 / 1 = 4584 (the remainder is 0, so 1 and 4584 are divisors of 4584)
4584 / 2 = 2292 (the remainder is 0, so 2 and 2292 are divisors of 4584)
4584 / 3 = 1528 (the remainder is 0, so 3 and 1528 are divisors of 4584)
...
4584 / 66 = 69.454545454545 (the remainder is 30, so 66 is not a divisor of 4584)
4584 / 67 = 68.417910447761 (the remainder is 28, so 67 is not a divisor of 4584)