What are the divisors of 2880?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 144, 160, 180, 192, 240, 288, 320, 360, 480, 576, 720, 960, 1440, 2880

There is a total of 42 positive divisors.
The sum of these divisors is 9906.
The arithmetic mean is 235.85714285714.

36 even divisors

2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 60, 64, 72, 80, 90, 96, 120, 144, 160, 180, 192, 240, 288, 320, 360, 480, 576, 720, 960, 1440, 2880

6 odd divisors

1, 3, 5, 9, 15, 45

How to compute the divisors of 2880?

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 2880 by each of the numbers from 1 to 2880 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)

2880 / 1 = 2880 (the remainder is 0, so 1 is a divisor of 2880)
2880 / 2 = 1440 (the remainder is 0, so 2 is a divisor of 2880)
2880 / 3 = 960 (the remainder is 0, so 3 is a divisor of 2880)
...
2880 / 2879 = 1.0003473428274 (the remainder is 1, so 2879 is not a divisor of 2880)
2880 / 2880 = 1 (the remainder is 0, so 2880 is a divisor of 2880)

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 2880 (i.e. 53.665631459995). 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 $\frac{N}{d} = D$ )

2880 / 1 = 2880 (the remainder is 0, so 1 and 2880 are divisors of 2880)
2880 / 2 = 1440 (the remainder is 0, so 2 and 1440 are divisors of 2880)
2880 / 3 = 960 (the remainder is 0, so 3 and 960 are divisors of 2880)
...
2880 / 52 = 55.384615384615 (the remainder is 20, so 52 is not a divisor of 2880)
2880 / 53 = 54.339622641509 (the remainder is 18, so 53 is not a divisor of 2880)