What are the divisors of 3660?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 61, 122, 183, 244, 305, 366, 610, 732, 915, 1220, 1830, 3660

There is a total of 24 positive divisors.
The sum of these divisors is 10416.
The arithmetic mean is 434.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 122, 244, 366, 610, 732, 1220, 1830, 3660

8 odd divisors

1, 3, 5, 15, 61, 183, 305, 915

How to compute the divisors of 3660?

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 3660 by each of the numbers from 1 to 3660 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)

3660 / 1 = 3660 (the remainder is 0, so 1 is a divisor of 3660)
3660 / 2 = 1830 (the remainder is 0, so 2 is a divisor of 3660)
3660 / 3 = 1220 (the remainder is 0, so 3 is a divisor of 3660)
...
3660 / 3659 = 1.0002732987155 (the remainder is 1, so 3659 is not a divisor of 3660)
3660 / 3660 = 1 (the remainder is 0, so 3660 is a divisor of 3660)

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 3660 (i.e. 60.497933849017). 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 $\frac{N}{d} = D$ )

3660 / 1 = 3660 (the remainder is 0, so 1 and 3660 are divisors of 3660)
3660 / 2 = 1830 (the remainder is 0, so 2 and 1830 are divisors of 3660)
3660 / 3 = 1220 (the remainder is 0, so 3 and 1220 are divisors of 3660)
...
3660 / 59 = 62.033898305085 (the remainder is 2, so 59 is not a divisor of 3660)
3660 / 60 = 61 (the remainder is 0, so 60 and 61 are divisors of 3660)