What are the divisors of 3365?

1, 5, 673, 3365

There is a total of 4 positive divisors.
The sum of these divisors is 4044.
The arithmetic mean is 1011.

4 odd divisors

1, 5, 673, 3365

How to compute the divisors of 3365?

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 3365 by each of the numbers from 1 to 3365 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)

3365 / 1 = 3365 (the remainder is 0, so 1 is a divisor of 3365)
3365 / 2 = 1682.5 (the remainder is 1, so 2 is not a divisor of 3365)
3365 / 3 = 1121.6666666667 (the remainder is 2, so 3 is not a divisor of 3365)
...
3365 / 3364 = 1.0002972651605 (the remainder is 1, so 3364 is not a divisor of 3365)
3365 / 3365 = 1 (the remainder is 0, so 3365 is a divisor of 3365)

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 3365 (i.e. 58.008620049093). 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 $\frac{N}{d} = D$ )

3365 / 1 = 3365 (the remainder is 0, so 1 and 3365 are divisors of 3365)
3365 / 2 = 1682.5 (the remainder is 1, so 2 is not a divisor of 3365)
3365 / 3 = 1121.6666666667 (the remainder is 2, so 3 is not a divisor of 3365)
...
3365 / 57 = 59.035087719298 (the remainder is 2, so 57 is not a divisor of 3365)
3365 / 58 = 58.01724137931 (the remainder is 1, so 58 is not a divisor of 3365)