What are the divisors of 4488?

1, 2, 3, 4, 6, 8, 11, 12, 17, 22, 24, 33, 34, 44, 51, 66, 68, 88, 102, 132, 136, 187, 204, 264, 374, 408, 561, 748, 1122, 1496, 2244, 4488

There is a total of 32 positive divisors.
The sum of these divisors is 12960.
The arithmetic mean is 405.

24 even divisors

2, 4, 6, 8, 12, 22, 24, 34, 44, 66, 68, 88, 102, 132, 136, 204, 264, 374, 408, 748, 1122, 1496, 2244, 4488

8 odd divisors

1, 3, 11, 17, 33, 51, 187, 561

How to compute the divisors of 4488?

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 4488 by each of the numbers from 1 to 4488 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)

4488 / 1 = 4488 (the remainder is 0, so 1 is a divisor of 4488)
4488 / 2 = 2244 (the remainder is 0, so 2 is a divisor of 4488)
4488 / 3 = 1496 (the remainder is 0, so 3 is a divisor of 4488)
...
4488 / 4487 = 1.0002228660575 (the remainder is 1, so 4487 is not a divisor of 4488)
4488 / 4488 = 1 (the remainder is 0, so 4488 is a divisor of 4488)

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 4488 (i.e. 66.992536897777). 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 $\frac{N}{d} = D$ )

4488 / 1 = 4488 (the remainder is 0, so 1 and 4488 are divisors of 4488)
4488 / 2 = 2244 (the remainder is 0, so 2 and 2244 are divisors of 4488)
4488 / 3 = 1496 (the remainder is 0, so 3 and 1496 are divisors of 4488)
...
4488 / 65 = 69.046153846154 (the remainder is 3, so 65 is not a divisor of 4488)
4488 / 66 = 68 (the remainder is 0, so 66 and 68 are divisors of 4488)