What are the divisors of 4389?

1, 3, 7, 11, 19, 21, 33, 57, 77, 133, 209, 231, 399, 627, 1463, 4389

There is a total of 16 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 480.

16 odd divisors

1, 3, 7, 11, 19, 21, 33, 57, 77, 133, 209, 231, 399, 627, 1463, 4389

How to compute the divisors of 4389?

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 4389 by each of the numbers from 1 to 4389 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)

4389 / 1 = 4389 (the remainder is 0, so 1 is a divisor of 4389)
4389 / 2 = 2194.5 (the remainder is 1, so 2 is not a divisor of 4389)
4389 / 3 = 1463 (the remainder is 0, so 3 is a divisor of 4389)
...
4389 / 4388 = 1.0002278942571 (the remainder is 1, so 4388 is not a divisor of 4389)
4389 / 4389 = 1 (the remainder is 0, so 4389 is a divisor of 4389)

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 4389 (i.e. 66.249528300208). 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 $\frac{N}{d} = D$ )

4389 / 1 = 4389 (the remainder is 0, so 1 and 4389 are divisors of 4389)
4389 / 2 = 2194.5 (the remainder is 1, so 2 is not a divisor of 4389)
4389 / 3 = 1463 (the remainder is 0, so 3 and 1463 are divisors of 4389)
...
4389 / 65 = 67.523076923077 (the remainder is 34, so 65 is not a divisor of 4389)
4389 / 66 = 66.5 (the remainder is 33, so 66 is not a divisor of 4389)