What are the divisors of 3363?

1, 3, 19, 57, 59, 177, 1121, 3363

There is a total of 8 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 600.

8 odd divisors

1, 3, 19, 57, 59, 177, 1121, 3363

How to compute the divisors of 3363?

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 3363 by each of the numbers from 1 to 3363 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)

3363 / 1 = 3363 (the remainder is 0, so 1 is a divisor of 3363)
3363 / 2 = 1681.5 (the remainder is 1, so 2 is not a divisor of 3363)
3363 / 3 = 1121 (the remainder is 0, so 3 is a divisor of 3363)
...
3363 / 3362 = 1.0002974419988 (the remainder is 1, so 3362 is not a divisor of 3363)
3363 / 3363 = 1 (the remainder is 0, so 3363 is a divisor of 3363)

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 3363 (i.e. 57.991378669592). 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 $\frac{N}{d} = D$ )

3363 / 1 = 3363 (the remainder is 0, so 1 and 3363 are divisors of 3363)
3363 / 2 = 1681.5 (the remainder is 1, so 2 is not a divisor of 3363)
3363 / 3 = 1121 (the remainder is 0, so 3 and 1121 are divisors of 3363)
...
3363 / 56 = 60.053571428571 (the remainder is 3, so 56 is not a divisor of 3363)
3363 / 57 = 59 (the remainder is 0, so 57 and 59 are divisors of 3363)