What are the divisors of 3361?

1, 3361

There is a total of 2 positive divisors.
The sum of these divisors is 3362.
The arithmetic mean is 1681.

2 odd divisors

1, 3361

How to compute the divisors of 3361?

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 3361 by each of the numbers from 1 to 3361 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)

3361 / 1 = 3361 (the remainder is 0, so 1 is a divisor of 3361)
3361 / 2 = 1680.5 (the remainder is 1, so 2 is not a divisor of 3361)
3361 / 3 = 1120.3333333333 (the remainder is 1, so 3 is not a divisor of 3361)
...
3361 / 3360 = 1.0002976190476 (the remainder is 1, so 3360 is not a divisor of 3361)
3361 / 3361 = 1 (the remainder is 0, so 3361 is a divisor of 3361)

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 3361 (i.e. 57.974132162543). 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 $\frac{N}{d} = D$ )

3361 / 1 = 3361 (the remainder is 0, so 1 and 3361 are divisors of 3361)
3361 / 2 = 1680.5 (the remainder is 1, so 2 is not a divisor of 3361)
3361 / 3 = 1120.3333333333 (the remainder is 1, so 3 is not a divisor of 3361)
...
3361 / 56 = 60.017857142857 (the remainder is 1, so 56 is not a divisor of 3361)
3361 / 57 = 58.964912280702 (the remainder is 55, so 57 is not a divisor of 3361)