What are the divisors of 4326?

1, 2, 3, 6, 7, 14, 21, 42, 103, 206, 309, 618, 721, 1442, 2163, 4326

There is a total of 16 positive divisors.
The sum of these divisors is 9984.
The arithmetic mean is 624.

8 even divisors

2, 6, 14, 42, 206, 618, 1442, 4326

8 odd divisors

1, 3, 7, 21, 103, 309, 721, 2163

How to compute the divisors of 4326?

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 4326 by each of the numbers from 1 to 4326 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)

4326 / 1 = 4326 (the remainder is 0, so 1 is a divisor of 4326)
4326 / 2 = 2163 (the remainder is 0, so 2 is a divisor of 4326)
4326 / 3 = 1442 (the remainder is 0, so 3 is a divisor of 4326)
...
4326 / 4325 = 1.0002312138728 (the remainder is 1, so 4325 is not a divisor of 4326)
4326 / 4326 = 1 (the remainder is 0, so 4326 is a divisor of 4326)

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 4326 (i.e. 65.772334609621). 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 $\frac{N}{d} = D$ )

4326 / 1 = 4326 (the remainder is 0, so 1 and 4326 are divisors of 4326)
4326 / 2 = 2163 (the remainder is 0, so 2 and 2163 are divisors of 4326)
4326 / 3 = 1442 (the remainder is 0, so 3 and 1442 are divisors of 4326)
...
4326 / 64 = 67.59375 (the remainder is 38, so 64 is not a divisor of 4326)
4326 / 65 = 66.553846153846 (the remainder is 36, so 65 is not a divisor of 4326)