What are the divisors of 3321?

1, 3, 9, 27, 41, 81, 123, 369, 1107, 3321

There is a total of 10 positive divisors.
The sum of these divisors is 5082.
The arithmetic mean is 508.2.

10 odd divisors

1, 3, 9, 27, 41, 81, 123, 369, 1107, 3321

How to compute the divisors of 3321?

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 3321 by each of the numbers from 1 to 3321 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)

3321 / 1 = 3321 (the remainder is 0, so 1 is a divisor of 3321)
3321 / 2 = 1660.5 (the remainder is 1, so 2 is not a divisor of 3321)
3321 / 3 = 1107 (the remainder is 0, so 3 is a divisor of 3321)
...
3321 / 3320 = 1.0003012048193 (the remainder is 1, so 3320 is not a divisor of 3321)
3321 / 3321 = 1 (the remainder is 0, so 3321 is a divisor of 3321)

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 3321 (i.e. 57.628118136896). 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 $\frac{N}{d} = D$ )

3321 / 1 = 3321 (the remainder is 0, so 1 and 3321 are divisors of 3321)
3321 / 2 = 1660.5 (the remainder is 1, so 2 is not a divisor of 3321)
3321 / 3 = 1107 (the remainder is 0, so 3 and 1107 are divisors of 3321)
...
3321 / 56 = 59.303571428571 (the remainder is 17, so 56 is not a divisor of 3321)
3321 / 57 = 58.263157894737 (the remainder is 15, so 57 is not a divisor of 3321)