What are the divisors of 2400?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400

There is a total of 36 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 217.

30 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 50, 60, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400

6 odd divisors

1, 3, 5, 15, 25, 75

How to compute the divisors of 2400?

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 2400 by each of the numbers from 1 to 2400 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)

2400 / 1 = 2400 (the remainder is 0, so 1 is a divisor of 2400)
2400 / 2 = 1200 (the remainder is 0, so 2 is a divisor of 2400)
2400 / 3 = 800 (the remainder is 0, so 3 is a divisor of 2400)
...
2400 / 2399 = 1.0004168403501 (the remainder is 1, so 2399 is not a divisor of 2400)
2400 / 2400 = 1 (the remainder is 0, so 2400 is a divisor of 2400)

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 2400 (i.e. 48.989794855664). 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 $\frac{N}{d} = D$ )

2400 / 1 = 2400 (the remainder is 0, so 1 and 2400 are divisors of 2400)
2400 / 2 = 1200 (the remainder is 0, so 2 and 1200 are divisors of 2400)
2400 / 3 = 800 (the remainder is 0, so 3 and 800 are divisors of 2400)
...
2400 / 47 = 51.063829787234 (the remainder is 3, so 47 is not a divisor of 2400)
2400 / 48 = 50 (the remainder is 0, so 48 and 50 are divisors of 2400)