What are the divisors of 3330?

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 37, 45, 74, 90, 111, 185, 222, 333, 370, 555, 666, 1110, 1665, 3330

There is a total of 24 positive divisors.
The sum of these divisors is 8892.
The arithmetic mean is 370.5.

12 even divisors

2, 6, 10, 18, 30, 74, 90, 222, 370, 666, 1110, 3330

12 odd divisors

1, 3, 5, 9, 15, 37, 45, 111, 185, 333, 555, 1665

How to compute the divisors of 3330?

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 3330 by each of the numbers from 1 to 3330 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)

3330 / 1 = 3330 (the remainder is 0, so 1 is a divisor of 3330)
3330 / 2 = 1665 (the remainder is 0, so 2 is a divisor of 3330)
3330 / 3 = 1110 (the remainder is 0, so 3 is a divisor of 3330)
...
3330 / 3329 = 1.0003003905077 (the remainder is 1, so 3329 is not a divisor of 3330)
3330 / 3330 = 1 (the remainder is 0, so 3330 is a divisor of 3330)

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 3330 (i.e. 57.706152185014). 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 $\frac{N}{d} = D$ )

3330 / 1 = 3330 (the remainder is 0, so 1 and 3330 are divisors of 3330)
3330 / 2 = 1665 (the remainder is 0, so 2 and 1665 are divisors of 3330)
3330 / 3 = 1110 (the remainder is 0, so 3 and 1110 are divisors of 3330)
...
3330 / 56 = 59.464285714286 (the remainder is 26, so 56 is not a divisor of 3330)
3330 / 57 = 58.421052631579 (the remainder is 24, so 57 is not a divisor of 3330)