What are the divisors of 3312?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 552, 828, 1104, 1656, 3312

There is a total of 30 positive divisors.
The sum of these divisors is 9672.
The arithmetic mean is 322.4.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 46, 48, 72, 92, 138, 144, 184, 276, 368, 414, 552, 828, 1104, 1656, 3312

6 odd divisors

1, 3, 9, 23, 69, 207

How to compute the divisors of 3312?

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 3312 by each of the numbers from 1 to 3312 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)

3312 / 1 = 3312 (the remainder is 0, so 1 is a divisor of 3312)
3312 / 2 = 1656 (the remainder is 0, so 2 is a divisor of 3312)
3312 / 3 = 1104 (the remainder is 0, so 3 is a divisor of 3312)
...
3312 / 3311 = 1.0003020235578 (the remainder is 1, so 3311 is not a divisor of 3312)
3312 / 3312 = 1 (the remainder is 0, so 3312 is a divisor of 3312)

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 3312 (i.e. 57.549978279753). 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 $\frac{N}{d} = D$ )

3312 / 1 = 3312 (the remainder is 0, so 1 and 3312 are divisors of 3312)
3312 / 2 = 1656 (the remainder is 0, so 2 and 1656 are divisors of 3312)
3312 / 3 = 1104 (the remainder is 0, so 3 and 1104 are divisors of 3312)
...
3312 / 56 = 59.142857142857 (the remainder is 8, so 56 is not a divisor of 3312)
3312 / 57 = 58.105263157895 (the remainder is 6, so 57 is not a divisor of 3312)