What are the divisors of 3327?

1, 3, 1109, 3327

There is a total of 4 positive divisors.
The sum of these divisors is 4440.
The arithmetic mean is 1110.

4 odd divisors

1, 3, 1109, 3327

How to compute the divisors of 3327?

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 3327 by each of the numbers from 1 to 3327 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)

3327 / 1 = 3327 (the remainder is 0, so 1 is a divisor of 3327)
3327 / 2 = 1663.5 (the remainder is 1, so 2 is not a divisor of 3327)
3327 / 3 = 1109 (the remainder is 0, so 3 is a divisor of 3327)
...
3327 / 3326 = 1.0003006614552 (the remainder is 1, so 3326 is not a divisor of 3327)
3327 / 3327 = 1 (the remainder is 0, so 3327 is a divisor of 3327)

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 3327 (i.e. 57.680152565679). 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 $\frac{N}{d} = D$ )

3327 / 1 = 3327 (the remainder is 0, so 1 and 3327 are divisors of 3327)
3327 / 2 = 1663.5 (the remainder is 1, so 2 is not a divisor of 3327)
3327 / 3 = 1109 (the remainder is 0, so 3 and 1109 are divisors of 3327)
...
3327 / 56 = 59.410714285714 (the remainder is 23, so 56 is not a divisor of 3327)
3327 / 57 = 58.368421052632 (the remainder is 21, so 57 is not a divisor of 3327)