What are the divisors of 1320?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320

There is a total of 32 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 135.

24 even divisors

2, 4, 6, 8, 10, 12, 20, 22, 24, 30, 40, 44, 60, 66, 88, 110, 120, 132, 220, 264, 330, 440, 660, 1320

8 odd divisors

1, 3, 5, 11, 15, 33, 55, 165

How to compute the divisors of 1320?

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 1320 by each of the numbers from 1 to 1320 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)

1320 / 1 = 1320 (the remainder is 0, so 1 is a divisor of 1320)
1320 / 2 = 660 (the remainder is 0, so 2 is a divisor of 1320)
1320 / 3 = 440 (the remainder is 0, so 3 is a divisor of 1320)
...
1320 / 1319 = 1.0007581501137 (the remainder is 1, so 1319 is not a divisor of 1320)
1320 / 1320 = 1 (the remainder is 0, so 1320 is a divisor of 1320)

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 1320 (i.e. 36.33180424917). 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 $\frac{N}{d} = D$ )

1320 / 1 = 1320 (the remainder is 0, so 1 and 1320 are divisors of 1320)
1320 / 2 = 660 (the remainder is 0, so 2 and 660 are divisors of 1320)
1320 / 3 = 440 (the remainder is 0, so 3 and 440 are divisors of 1320)
...
1320 / 35 = 37.714285714286 (the remainder is 25, so 35 is not a divisor of 1320)
1320 / 36 = 36.666666666667 (the remainder is 24, so 36 is not a divisor of 1320)