What are the divisors of 8280?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 23, 24, 30, 36, 40, 45, 46, 60, 69, 72, 90, 92, 115, 120, 138, 180, 184, 207, 230, 276, 345, 360, 414, 460, 552, 690, 828, 920, 1035, 1380, 1656, 2070, 2760, 4140, 8280

There is a total of 48 positive divisors.
The sum of these divisors is 28080.
The arithmetic mean is 585.

36 even divisors

2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 40, 46, 60, 72, 90, 92, 120, 138, 180, 184, 230, 276, 360, 414, 460, 552, 690, 828, 920, 1380, 1656, 2070, 2760, 4140, 8280

12 odd divisors

1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345, 1035

How to compute the divisors of 8280?

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 8280 by each of the numbers from 1 to 8280 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)

8280 / 1 = 8280 (the remainder is 0, so 1 is a divisor of 8280)
8280 / 2 = 4140 (the remainder is 0, so 2 is a divisor of 8280)
8280 / 3 = 2760 (the remainder is 0, so 3 is a divisor of 8280)
...
8280 / 8279 = 1.0001207875347 (the remainder is 1, so 8279 is not a divisor of 8280)
8280 / 8280 = 1 (the remainder is 0, so 8280 is a divisor of 8280)

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 8280 (i.e. 90.994505328619). 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 $\frac{N}{d} = D$ )

8280 / 1 = 8280 (the remainder is 0, so 1 and 8280 are divisors of 8280)
8280 / 2 = 4140 (the remainder is 0, so 2 and 4140 are divisors of 8280)
8280 / 3 = 2760 (the remainder is 0, so 3 and 2760 are divisors of 8280)
...
8280 / 89 = 93.033707865169 (the remainder is 3, so 89 is not a divisor of 8280)
8280 / 90 = 92 (the remainder is 0, so 90 and 92 are divisors of 8280)