What are the divisors of 4368?

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 39, 42, 48, 52, 56, 78, 84, 91, 104, 112, 156, 168, 182, 208, 273, 312, 336, 364, 546, 624, 728, 1092, 1456, 2184, 4368

There is a total of 40 positive divisors.
The sum of these divisors is 13888.
The arithmetic mean is 347.2.

32 even divisors

2, 4, 6, 8, 12, 14, 16, 24, 26, 28, 42, 48, 52, 56, 78, 84, 104, 112, 156, 168, 182, 208, 312, 336, 364, 546, 624, 728, 1092, 1456, 2184, 4368

8 odd divisors

1, 3, 7, 13, 21, 39, 91, 273

How to compute the divisors of 4368?

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 4368 by each of the numbers from 1 to 4368 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)

4368 / 1 = 4368 (the remainder is 0, so 1 is a divisor of 4368)
4368 / 2 = 2184 (the remainder is 0, so 2 is a divisor of 4368)
4368 / 3 = 1456 (the remainder is 0, so 3 is a divisor of 4368)
...
4368 / 4367 = 1.0002289901534 (the remainder is 1, so 4367 is not a divisor of 4368)
4368 / 4368 = 1 (the remainder is 0, so 4368 is a divisor of 4368)

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 4368 (i.e. 66.090846567433). 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 $\frac{N}{d} = D$ )

4368 / 1 = 4368 (the remainder is 0, so 1 and 4368 are divisors of 4368)
4368 / 2 = 2184 (the remainder is 0, so 2 and 2184 are divisors of 4368)
4368 / 3 = 1456 (the remainder is 0, so 3 and 1456 are divisors of 4368)
...
4368 / 65 = 67.2 (the remainder is 13, so 65 is not a divisor of 4368)
4368 / 66 = 66.181818181818 (the remainder is 12, so 66 is not a divisor of 4368)