What are the divisors of 2433?

1, 3, 811, 2433

There is a total of 4 positive divisors.
The sum of these divisors is 3248.
The arithmetic mean is 812.

4 odd divisors

1, 3, 811, 2433

How to compute the divisors of 2433?

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 2433 by each of the numbers from 1 to 2433 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)

2433 / 1 = 2433 (the remainder is 0, so 1 is a divisor of 2433)
2433 / 2 = 1216.5 (the remainder is 1, so 2 is not a divisor of 2433)
2433 / 3 = 811 (the remainder is 0, so 3 is a divisor of 2433)
...
2433 / 2432 = 1.0004111842105 (the remainder is 1, so 2432 is not a divisor of 2433)
2433 / 2433 = 1 (the remainder is 0, so 2433 is a divisor of 2433)

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 2433 (i.e. 49.325449820554). 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 $\frac{N}{d} = D$ )

2433 / 1 = 2433 (the remainder is 0, so 1 and 2433 are divisors of 2433)
2433 / 2 = 1216.5 (the remainder is 1, so 2 is not a divisor of 2433)
2433 / 3 = 811 (the remainder is 0, so 3 and 811 are divisors of 2433)
...
2433 / 48 = 50.6875 (the remainder is 33, so 48 is not a divisor of 2433)
2433 / 49 = 49.65306122449 (the remainder is 32, so 49 is not a divisor of 2433)