What are the divisors of 3393?

1, 3, 9, 13, 29, 39, 87, 117, 261, 377, 1131, 3393

There is a total of 12 positive divisors.
The sum of these divisors is 5460.
The arithmetic mean is 455.

12 odd divisors

1, 3, 9, 13, 29, 39, 87, 117, 261, 377, 1131, 3393

How to compute the divisors of 3393?

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 3393 by each of the numbers from 1 to 3393 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)

3393 / 1 = 3393 (the remainder is 0, so 1 is a divisor of 3393)
3393 / 2 = 1696.5 (the remainder is 1, so 2 is not a divisor of 3393)
3393 / 3 = 1131 (the remainder is 0, so 3 is a divisor of 3393)
...
3393 / 3392 = 1.0002948113208 (the remainder is 1, so 3392 is not a divisor of 3393)
3393 / 3393 = 1 (the remainder is 0, so 3393 is a divisor of 3393)

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 3393 (i.e. 58.249463516843). 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 $\frac{N}{d} = D$ )

3393 / 1 = 3393 (the remainder is 0, so 1 and 3393 are divisors of 3393)
3393 / 2 = 1696.5 (the remainder is 1, so 2 is not a divisor of 3393)
3393 / 3 = 1131 (the remainder is 0, so 3 and 1131 are divisors of 3393)
...
3393 / 57 = 59.526315789474 (the remainder is 30, so 57 is not a divisor of 3393)
3393 / 58 = 58.5 (the remainder is 29, so 58 is not a divisor of 3393)