What are the divisors of 3663?

1, 3, 9, 11, 33, 37, 99, 111, 333, 407, 1221, 3663

There is a total of 12 positive divisors.
The sum of these divisors is 5928.
The arithmetic mean is 494.

12 odd divisors

1, 3, 9, 11, 33, 37, 99, 111, 333, 407, 1221, 3663

How to compute the divisors of 3663?

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 3663 by each of the numbers from 1 to 3663 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)

3663 / 1 = 3663 (the remainder is 0, so 1 is a divisor of 3663)
3663 / 2 = 1831.5 (the remainder is 1, so 2 is not a divisor of 3663)
3663 / 3 = 1221 (the remainder is 0, so 3 is a divisor of 3663)
...
3663 / 3662 = 1.0002730748225 (the remainder is 1, so 3662 is not a divisor of 3663)
3663 / 3663 = 1 (the remainder is 0, so 3663 is a divisor of 3663)

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 3663 (i.e. 60.522723005496). 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 $\frac{N}{d} = D$ )

3663 / 1 = 3663 (the remainder is 0, so 1 and 3663 are divisors of 3663)
3663 / 2 = 1831.5 (the remainder is 1, so 2 is not a divisor of 3663)
3663 / 3 = 1221 (the remainder is 0, so 3 and 1221 are divisors of 3663)
...
3663 / 59 = 62.084745762712 (the remainder is 5, so 59 is not a divisor of 3663)
3663 / 60 = 61.05 (the remainder is 3, so 60 is not a divisor of 3663)