What are the divisors of 3305?

1, 5, 661, 3305

There is a total of 4 positive divisors.
The sum of these divisors is 3972.
The arithmetic mean is 993.

4 odd divisors

1, 5, 661, 3305

How to compute the divisors of 3305?

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 3305 by each of the numbers from 1 to 3305 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)

3305 / 1 = 3305 (the remainder is 0, so 1 is a divisor of 3305)
3305 / 2 = 1652.5 (the remainder is 1, so 2 is not a divisor of 3305)
3305 / 3 = 1101.6666666667 (the remainder is 2, so 3 is not a divisor of 3305)
...
3305 / 3304 = 1.0003026634383 (the remainder is 1, so 3304 is not a divisor of 3305)
3305 / 3305 = 1 (the remainder is 0, so 3305 is a divisor of 3305)

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 3305 (i.e. 57.489129407219). 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 $\frac{N}{d} = D$ )

3305 / 1 = 3305 (the remainder is 0, so 1 and 3305 are divisors of 3305)
3305 / 2 = 1652.5 (the remainder is 1, so 2 is not a divisor of 3305)
3305 / 3 = 1101.6666666667 (the remainder is 2, so 3 is not a divisor of 3305)
...
3305 / 56 = 59.017857142857 (the remainder is 1, so 56 is not a divisor of 3305)
3305 / 57 = 57.982456140351 (the remainder is 56, so 57 is not a divisor of 3305)