What are the divisors of 3303?

1, 3, 9, 367, 1101, 3303

There is a total of 6 positive divisors.
The sum of these divisors is 4784.
The arithmetic mean is 797.33333333333.

6 odd divisors

1, 3, 9, 367, 1101, 3303

How to compute the divisors of 3303?

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 3303 by each of the numbers from 1 to 3303 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)

3303 / 1 = 3303 (the remainder is 0, so 1 is a divisor of 3303)
3303 / 2 = 1651.5 (the remainder is 1, so 2 is not a divisor of 3303)
3303 / 3 = 1101 (the remainder is 0, so 3 is a divisor of 3303)
...
3303 / 3302 = 1.0003028467595 (the remainder is 1, so 3302 is not a divisor of 3303)
3303 / 3303 = 1 (the remainder is 0, so 3303 is a divisor of 3303)

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 3303 (i.e. 57.471732182004). 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 $\frac{N}{d} = D$ )

3303 / 1 = 3303 (the remainder is 0, so 1 and 3303 are divisors of 3303)
3303 / 2 = 1651.5 (the remainder is 1, so 2 is not a divisor of 3303)
3303 / 3 = 1101 (the remainder is 0, so 3 and 1101 are divisors of 3303)
...
3303 / 56 = 58.982142857143 (the remainder is 55, so 56 is not a divisor of 3303)
3303 / 57 = 57.947368421053 (the remainder is 54, so 57 is not a divisor of 3303)