What are the divisors of 2484?

1, 2, 3, 4, 6, 9, 12, 18, 23, 27, 36, 46, 54, 69, 92, 108, 138, 207, 276, 414, 621, 828, 1242, 2484

There is a total of 24 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 280.

16 even divisors

2, 4, 6, 12, 18, 36, 46, 54, 92, 108, 138, 276, 414, 828, 1242, 2484

8 odd divisors

1, 3, 9, 23, 27, 69, 207, 621

How to compute the divisors of 2484?

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 2484 by each of the numbers from 1 to 2484 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)

2484 / 1 = 2484 (the remainder is 0, so 1 is a divisor of 2484)
2484 / 2 = 1242 (the remainder is 0, so 2 is a divisor of 2484)
2484 / 3 = 828 (the remainder is 0, so 3 is a divisor of 2484)
...
2484 / 2483 = 1.0004027386226 (the remainder is 1, so 2483 is not a divisor of 2484)
2484 / 2484 = 1 (the remainder is 0, so 2484 is a divisor of 2484)

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 2484 (i.e. 49.839743177508). 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 $\frac{N}{d} = D$ )

2484 / 1 = 2484 (the remainder is 0, so 1 and 2484 are divisors of 2484)
2484 / 2 = 1242 (the remainder is 0, so 2 and 1242 are divisors of 2484)
2484 / 3 = 828 (the remainder is 0, so 3 and 828 are divisors of 2484)
...
2484 / 48 = 51.75 (the remainder is 36, so 48 is not a divisor of 2484)
2484 / 49 = 50.69387755102 (the remainder is 34, so 49 is not a divisor of 2484)