What are the divisors of 4608?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1152, 1536, 2304, 4608

There is a total of 30 positive divisors.
The sum of these divisors is 13299.
The arithmetic mean is 443.3.

27 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1152, 1536, 2304, 4608

3 odd divisors

1, 3, 9

How to compute the divisors of 4608?

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 4608 by each of the numbers from 1 to 4608 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)

4608 / 1 = 4608 (the remainder is 0, so 1 is a divisor of 4608)
4608 / 2 = 2304 (the remainder is 0, so 2 is a divisor of 4608)
4608 / 3 = 1536 (the remainder is 0, so 3 is a divisor of 4608)
...
4608 / 4607 = 1.0002170609941 (the remainder is 1, so 4607 is not a divisor of 4608)
4608 / 4608 = 1 (the remainder is 0, so 4608 is a divisor of 4608)

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 4608 (i.e. 67.882250993909). 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 $\frac{N}{d} = D$ )

4608 / 1 = 4608 (the remainder is 0, so 1 and 4608 are divisors of 4608)
4608 / 2 = 2304 (the remainder is 0, so 2 and 2304 are divisors of 4608)
4608 / 3 = 1536 (the remainder is 0, so 3 and 1536 are divisors of 4608)
...
4608 / 66 = 69.818181818182 (the remainder is 54, so 66 is not a divisor of 4608)
4608 / 67 = 68.776119402985 (the remainder is 52, so 67 is not a divisor of 4608)