What are the divisors of 3309?

1, 3, 1103, 3309

There is a total of 4 positive divisors.
The sum of these divisors is 4416.
The arithmetic mean is 1104.

4 odd divisors

1, 3, 1103, 3309

How to compute the divisors of 3309?

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 3309 by each of the numbers from 1 to 3309 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)

3309 / 1 = 3309 (the remainder is 0, so 1 is a divisor of 3309)
3309 / 2 = 1654.5 (the remainder is 1, so 2 is not a divisor of 3309)
3309 / 3 = 1103 (the remainder is 0, so 3 is a divisor of 3309)
...
3309 / 3308 = 1.0003022974607 (the remainder is 1, so 3308 is not a divisor of 3309)
3309 / 3309 = 1 (the remainder is 0, so 3309 is a divisor of 3309)

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 3309 (i.e. 57.523908073079). 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 $\frac{N}{d} = D$ )

3309 / 1 = 3309 (the remainder is 0, so 1 and 3309 are divisors of 3309)
3309 / 2 = 1654.5 (the remainder is 1, so 2 is not a divisor of 3309)
3309 / 3 = 1103 (the remainder is 0, so 3 and 1103 are divisors of 3309)
...
3309 / 56 = 59.089285714286 (the remainder is 5, so 56 is not a divisor of 3309)
3309 / 57 = 58.052631578947 (the remainder is 3, so 57 is not a divisor of 3309)