What are the divisors of 3600?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600

There is a total of 45 positive divisors.
The sum of these divisors is 12493.
The arithmetic mean is 277.62222222222.

36 even divisors

2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 48, 50, 60, 72, 80, 90, 100, 120, 144, 150, 180, 200, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600

9 odd divisors

1, 3, 5, 9, 15, 25, 45, 75, 225

How to compute the divisors of 3600?

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 3600 by each of the numbers from 1 to 3600 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)

3600 / 1 = 3600 (the remainder is 0, so 1 is a divisor of 3600)
3600 / 2 = 1800 (the remainder is 0, so 2 is a divisor of 3600)
3600 / 3 = 1200 (the remainder is 0, so 3 is a divisor of 3600)
...
3600 / 3599 = 1.0002778549597 (the remainder is 1, so 3599 is not a divisor of 3600)
3600 / 3600 = 1 (the remainder is 0, so 3600 is a divisor of 3600)

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 3600 (i.e. 60). 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 $\frac{N}{d} = D$ )

3600 / 1 = 3600 (the remainder is 0, so 1 and 3600 are divisors of 3600)
3600 / 2 = 1800 (the remainder is 0, so 2 and 1800 are divisors of 3600)
3600 / 3 = 1200 (the remainder is 0, so 3 and 1200 are divisors of 3600)
...
3600 / 59 = 61.016949152542 (the remainder is 1, so 59 is not a divisor of 3600)
3600 / 60 = 60 (the remainder is 0, so 60 and 60 are divisors of 3600)