What are the divisors of 4464?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 31, 36, 48, 62, 72, 93, 124, 144, 186, 248, 279, 372, 496, 558, 744, 1116, 1488, 2232, 4464

There is a total of 30 positive divisors.
The sum of these divisors is 12896.
The arithmetic mean is 429.86666666667.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 62, 72, 124, 144, 186, 248, 372, 496, 558, 744, 1116, 1488, 2232, 4464

6 odd divisors

1, 3, 9, 31, 93, 279

How to compute the divisors of 4464?

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 4464 by each of the numbers from 1 to 4464 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)

4464 / 1 = 4464 (the remainder is 0, so 1 is a divisor of 4464)
4464 / 2 = 2232 (the remainder is 0, so 2 is a divisor of 4464)
4464 / 3 = 1488 (the remainder is 0, so 3 is a divisor of 4464)
...
4464 / 4463 = 1.0002240645306 (the remainder is 1, so 4463 is not a divisor of 4464)
4464 / 4464 = 1 (the remainder is 0, so 4464 is a divisor of 4464)

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 4464 (i.e. 66.81317235396). 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 $\frac{N}{d} = D$ )

4464 / 1 = 4464 (the remainder is 0, so 1 and 4464 are divisors of 4464)
4464 / 2 = 2232 (the remainder is 0, so 2 and 2232 are divisors of 4464)
4464 / 3 = 1488 (the remainder is 0, so 3 and 1488 are divisors of 4464)
...
4464 / 65 = 68.676923076923 (the remainder is 44, so 65 is not a divisor of 4464)
4464 / 66 = 67.636363636364 (the remainder is 42, so 66 is not a divisor of 4464)