What are the divisors of 4392?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 61, 72, 122, 183, 244, 366, 488, 549, 732, 1098, 1464, 2196, 4392

There is a total of 24 positive divisors.
The sum of these divisors is 12090.
The arithmetic mean is 503.75.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 122, 244, 366, 488, 732, 1098, 1464, 2196, 4392

6 odd divisors

1, 3, 9, 61, 183, 549

How to compute the divisors of 4392?

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 4392 by each of the numbers from 1 to 4392 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)

4392 / 1 = 4392 (the remainder is 0, so 1 is a divisor of 4392)
4392 / 2 = 2196 (the remainder is 0, so 2 is a divisor of 4392)
4392 / 3 = 1464 (the remainder is 0, so 3 is a divisor of 4392)
...
4392 / 4391 = 1.0002277385561 (the remainder is 1, so 4391 is not a divisor of 4392)
4392 / 4392 = 1 (the remainder is 0, so 4392 is a divisor of 4392)

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 4392 (i.e. 66.272166103124). 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 $\frac{N}{d} = D$ )

4392 / 1 = 4392 (the remainder is 0, so 1 and 4392 are divisors of 4392)
4392 / 2 = 2196 (the remainder is 0, so 2 and 2196 are divisors of 4392)
4392 / 3 = 1464 (the remainder is 0, so 3 and 1464 are divisors of 4392)
...
4392 / 65 = 67.569230769231 (the remainder is 37, so 65 is not a divisor of 4392)
4392 / 66 = 66.545454545455 (the remainder is 36, so 66 is not a divisor of 4392)