What are the divisors of 2430?

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430

There is a total of 24 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 273.

12 even divisors

2, 6, 10, 18, 30, 54, 90, 162, 270, 486, 810, 2430

12 odd divisors

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215

How to compute the divisors of 2430?

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 2430 by each of the numbers from 1 to 2430 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)

2430 / 1 = 2430 (the remainder is 0, so 1 is a divisor of 2430)
2430 / 2 = 1215 (the remainder is 0, so 2 is a divisor of 2430)
2430 / 3 = 810 (the remainder is 0, so 3 is a divisor of 2430)
...
2430 / 2429 = 1.0004116920543 (the remainder is 1, so 2429 is not a divisor of 2430)
2430 / 2430 = 1 (the remainder is 0, so 2430 is a divisor of 2430)

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 2430 (i.e. 49.295030175465). 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 $\frac{N}{d} = D$ )

2430 / 1 = 2430 (the remainder is 0, so 1 and 2430 are divisors of 2430)
2430 / 2 = 1215 (the remainder is 0, so 2 and 1215 are divisors of 2430)
2430 / 3 = 810 (the remainder is 0, so 3 and 810 are divisors of 2430)
...
2430 / 48 = 50.625 (the remainder is 30, so 48 is not a divisor of 2430)
2430 / 49 = 49.591836734694 (the remainder is 29, so 49 is not a divisor of 2430)