What are the divisors of 3684?

1, 2, 3, 4, 6, 12, 307, 614, 921, 1228, 1842, 3684

There is a total of 12 positive divisors.
The sum of these divisors is 8624.
The arithmetic mean is 718.66666666667.

8 even divisors

2, 4, 6, 12, 614, 1228, 1842, 3684

4 odd divisors

1, 3, 307, 921

How to compute the divisors of 3684?

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 3684 by each of the numbers from 1 to 3684 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)

3684 / 1 = 3684 (the remainder is 0, so 1 is a divisor of 3684)
3684 / 2 = 1842 (the remainder is 0, so 2 is a divisor of 3684)
3684 / 3 = 1228 (the remainder is 0, so 3 is a divisor of 3684)
...
3684 / 3683 = 1.0002715177844 (the remainder is 1, so 3683 is not a divisor of 3684)
3684 / 3684 = 1 (the remainder is 0, so 3684 is a divisor of 3684)

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 3684 (i.e. 60.695963621974). 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 $\frac{N}{d} = D$ )

3684 / 1 = 3684 (the remainder is 0, so 1 and 3684 are divisors of 3684)
3684 / 2 = 1842 (the remainder is 0, so 2 and 1842 are divisors of 3684)
3684 / 3 = 1228 (the remainder is 0, so 3 and 1228 are divisors of 3684)
...
3684 / 59 = 62.440677966102 (the remainder is 26, so 59 is not a divisor of 3684)
3684 / 60 = 61.4 (the remainder is 24, so 60 is not a divisor of 3684)