What are the divisors of 3301?

1, 3301

There is a total of 2 positive divisors.
The sum of these divisors is 3302.
The arithmetic mean is 1651.

2 odd divisors

1, 3301

How to compute the divisors of 3301?

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 3301 by each of the numbers from 1 to 3301 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)

3301 / 1 = 3301 (the remainder is 0, so 1 is a divisor of 3301)
3301 / 2 = 1650.5 (the remainder is 1, so 2 is not a divisor of 3301)
3301 / 3 = 1100.3333333333 (the remainder is 1, so 3 is not a divisor of 3301)
...
3301 / 3300 = 1.000303030303 (the remainder is 1, so 3300 is not a divisor of 3301)
3301 / 3301 = 1 (the remainder is 0, so 3301 is a divisor of 3301)

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 3301 (i.e. 57.454329688893). 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 $\frac{N}{d} = D$ )

3301 / 1 = 3301 (the remainder is 0, so 1 and 3301 are divisors of 3301)
3301 / 2 = 1650.5 (the remainder is 1, so 2 is not a divisor of 3301)
3301 / 3 = 1100.3333333333 (the remainder is 1, so 3 is not a divisor of 3301)
...
3301 / 56 = 58.946428571429 (the remainder is 53, so 56 is not a divisor of 3301)
3301 / 57 = 57.912280701754 (the remainder is 52, so 57 is not a divisor of 3301)