What are the divisors of 3385?

1, 5, 677, 3385

There is a total of 4 positive divisors.
The sum of these divisors is 4068.
The arithmetic mean is 1017.

4 odd divisors

1, 5, 677, 3385

How to compute the divisors of 3385?

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 3385 by each of the numbers from 1 to 3385 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)

3385 / 1 = 3385 (the remainder is 0, so 1 is a divisor of 3385)
3385 / 2 = 1692.5 (the remainder is 1, so 2 is not a divisor of 3385)
3385 / 3 = 1128.3333333333 (the remainder is 1, so 3 is not a divisor of 3385)
...
3385 / 3384 = 1.0002955082742 (the remainder is 1, so 3384 is not a divisor of 3385)
3385 / 3385 = 1 (the remainder is 0, so 3385 is a divisor of 3385)

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 3385 (i.e. 58.180752831155). 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 $\frac{N}{d} = D$ )

3385 / 1 = 3385 (the remainder is 0, so 1 and 3385 are divisors of 3385)
3385 / 2 = 1692.5 (the remainder is 1, so 2 is not a divisor of 3385)
3385 / 3 = 1128.3333333333 (the remainder is 1, so 3 is not a divisor of 3385)
...
3385 / 57 = 59.385964912281 (the remainder is 22, so 57 is not a divisor of 3385)
3385 / 58 = 58.362068965517 (the remainder is 21, so 58 is not a divisor of 3385)