What are the divisors of 4536?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 81, 84, 108, 126, 162, 168, 189, 216, 252, 324, 378, 504, 567, 648, 756, 1134, 1512, 2268, 4536

There is a total of 40 positive divisors.
The sum of these divisors is 14520.
The arithmetic mean is 363.

30 even divisors

2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 54, 56, 72, 84, 108, 126, 162, 168, 216, 252, 324, 378, 504, 648, 756, 1134, 1512, 2268, 4536

10 odd divisors

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

How to compute the divisors of 4536?

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 4536 by each of the numbers from 1 to 4536 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)

4536 / 1 = 4536 (the remainder is 0, so 1 is a divisor of 4536)
4536 / 2 = 2268 (the remainder is 0, so 2 is a divisor of 4536)
4536 / 3 = 1512 (the remainder is 0, so 3 is a divisor of 4536)
...
4536 / 4535 = 1.0002205071665 (the remainder is 1, so 4535 is not a divisor of 4536)
4536 / 4536 = 1 (the remainder is 0, so 4536 is a divisor of 4536)

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 4536 (i.e. 67.349832961931). 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 $\frac{N}{d} = D$ )

4536 / 1 = 4536 (the remainder is 0, so 1 and 4536 are divisors of 4536)
4536 / 2 = 2268 (the remainder is 0, so 2 and 2268 are divisors of 4536)
4536 / 3 = 1512 (the remainder is 0, so 3 and 1512 are divisors of 4536)
...
4536 / 66 = 68.727272727273 (the remainder is 48, so 66 is not a divisor of 4536)
4536 / 67 = 67.701492537313 (the remainder is 47, so 67 is not a divisor of 4536)