What are the divisors of 3383?

1, 17, 199, 3383

There is a total of 4 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 900.

4 odd divisors

1, 17, 199, 3383

How to compute the divisors of 3383?

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 3383 by each of the numbers from 1 to 3383 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)

3383 / 1 = 3383 (the remainder is 0, so 1 is a divisor of 3383)
3383 / 2 = 1691.5 (the remainder is 1, so 2 is not a divisor of 3383)
3383 / 3 = 1127.6666666667 (the remainder is 2, so 3 is not a divisor of 3383)
...
3383 / 3382 = 1.0002956830278 (the remainder is 1, so 3382 is not a divisor of 3383)
3383 / 3383 = 1 (the remainder is 0, so 3383 is a divisor of 3383)

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 3383 (i.e. 58.163562476863). 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 $\frac{N}{d} = D$ )

3383 / 1 = 3383 (the remainder is 0, so 1 and 3383 are divisors of 3383)
3383 / 2 = 1691.5 (the remainder is 1, so 2 is not a divisor of 3383)
3383 / 3 = 1127.6666666667 (the remainder is 2, so 3 is not a divisor of 3383)
...
3383 / 57 = 59.350877192982 (the remainder is 20, so 57 is not a divisor of 3383)
3383 / 58 = 58.327586206897 (the remainder is 19, so 58 is not a divisor of 3383)