What are the divisors of 3333?

1, 3, 11, 33, 101, 303, 1111, 3333

There is a total of 8 positive divisors.
The sum of these divisors is 4896.
The arithmetic mean is 612.

8 odd divisors

1, 3, 11, 33, 101, 303, 1111, 3333

How to compute the divisors of 3333?

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 3333 by each of the numbers from 1 to 3333 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)

3333 / 1 = 3333 (the remainder is 0, so 1 is a divisor of 3333)
3333 / 2 = 1666.5 (the remainder is 1, so 2 is not a divisor of 3333)
3333 / 3 = 1111 (the remainder is 0, so 3 is a divisor of 3333)
...
3333 / 3332 = 1.000300120048 (the remainder is 1, so 3332 is not a divisor of 3333)
3333 / 3333 = 1 (the remainder is 0, so 3333 is a divisor of 3333)

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 3333 (i.e. 57.732140095444). 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 $\frac{N}{d} = D$ )

3333 / 1 = 3333 (the remainder is 0, so 1 and 3333 are divisors of 3333)
3333 / 2 = 1666.5 (the remainder is 1, so 2 is not a divisor of 3333)
3333 / 3 = 1111 (the remainder is 0, so 3 and 1111 are divisors of 3333)
...
3333 / 56 = 59.517857142857 (the remainder is 29, so 56 is not a divisor of 3333)
3333 / 57 = 58.473684210526 (the remainder is 27, so 57 is not a divisor of 3333)