What are the divisors of 3360?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1120, 1680, 3360

There is a total of 48 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 252.

40 even divisors

2, 4, 6, 8, 10, 12, 14, 16, 20, 24, 28, 30, 32, 40, 42, 48, 56, 60, 70, 80, 84, 96, 112, 120, 140, 160, 168, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1120, 1680, 3360

8 odd divisors

1, 3, 5, 7, 15, 21, 35, 105

How to compute the divisors of 3360?

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 3360 by each of the numbers from 1 to 3360 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)

3360 / 1 = 3360 (the remainder is 0, so 1 is a divisor of 3360)
3360 / 2 = 1680 (the remainder is 0, so 2 is a divisor of 3360)
3360 / 3 = 1120 (the remainder is 0, so 3 is a divisor of 3360)
...
3360 / 3359 = 1.0002977076511 (the remainder is 1, so 3359 is not a divisor of 3360)
3360 / 3360 = 1 (the remainder is 0, so 3360 is a divisor of 3360)

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 3360 (i.e. 57.965506984758). 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 $\frac{N}{d} = D$ )

3360 / 1 = 3360 (the remainder is 0, so 1 and 3360 are divisors of 3360)
3360 / 2 = 1680 (the remainder is 0, so 2 and 1680 are divisors of 3360)
3360 / 3 = 1120 (the remainder is 0, so 3 and 1120 are divisors of 3360)
...
3360 / 56 = 60 (the remainder is 0, so 56 and 60 are divisors of 3360)
3360 / 57 = 58.947368421053 (the remainder is 54, so 57 is not a divisor of 3360)