What are the divisors of 3324?

1, 2, 3, 4, 6, 12, 277, 554, 831, 1108, 1662, 3324

There is a total of 12 positive divisors.
The sum of these divisors is 7784.
The arithmetic mean is 648.66666666667.

8 even divisors

2, 4, 6, 12, 554, 1108, 1662, 3324

4 odd divisors

1, 3, 277, 831

How to compute the divisors of 3324?

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 3324 by each of the numbers from 1 to 3324 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)

3324 / 1 = 3324 (the remainder is 0, so 1 is a divisor of 3324)
3324 / 2 = 1662 (the remainder is 0, so 2 is a divisor of 3324)
3324 / 3 = 1108 (the remainder is 0, so 3 is a divisor of 3324)
...
3324 / 3323 = 1.000300932892 (the remainder is 1, so 3323 is not a divisor of 3324)
3324 / 3324 = 1 (the remainder is 0, so 3324 is a divisor of 3324)

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 3324 (i.e. 57.654141221598). 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 $\frac{N}{d} = D$ )

3324 / 1 = 3324 (the remainder is 0, so 1 and 3324 are divisors of 3324)
3324 / 2 = 1662 (the remainder is 0, so 2 and 1662 are divisors of 3324)
3324 / 3 = 1108 (the remainder is 0, so 3 and 1108 are divisors of 3324)
...
3324 / 56 = 59.357142857143 (the remainder is 20, so 56 is not a divisor of 3324)
3324 / 57 = 58.315789473684 (the remainder is 18, so 57 is not a divisor of 3324)