What are the divisors of 8160?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 68, 80, 85, 96, 102, 120, 136, 160, 170, 204, 240, 255, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080, 8160

There is a total of 48 positive divisors.
The sum of these divisors is 27216.
The arithmetic mean is 567.

40 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 34, 40, 48, 60, 68, 80, 96, 102, 120, 136, 160, 170, 204, 240, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080, 8160

8 odd divisors

1, 3, 5, 15, 17, 51, 85, 255

How to compute the divisors of 8160?

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 8160 by each of the numbers from 1 to 8160 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)

8160 / 1 = 8160 (the remainder is 0, so 1 is a divisor of 8160)
8160 / 2 = 4080 (the remainder is 0, so 2 is a divisor of 8160)
8160 / 3 = 2720 (the remainder is 0, so 3 is a divisor of 8160)
...
8160 / 8159 = 1.0001225640397 (the remainder is 1, so 8159 is not a divisor of 8160)
8160 / 8160 = 1 (the remainder is 0, so 8160 is a divisor of 8160)

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 8160 (i.e. 90.33271832509). 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 $\frac{N}{d} = D$ )

8160 / 1 = 8160 (the remainder is 0, so 1 and 8160 are divisors of 8160)
8160 / 2 = 4080 (the remainder is 0, so 2 and 4080 are divisors of 8160)
8160 / 3 = 2720 (the remainder is 0, so 3 and 2720 are divisors of 8160)
...
8160 / 89 = 91.685393258427 (the remainder is 61, so 89 is not a divisor of 8160)
8160 / 90 = 90.666666666667 (the remainder is 60, so 90 is not a divisor of 8160)