What are the divisors of 8120?

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 29, 35, 40, 56, 58, 70, 116, 140, 145, 203, 232, 280, 290, 406, 580, 812, 1015, 1160, 1624, 2030, 4060, 8120

There is a total of 32 positive divisors.
The sum of these divisors is 21600.
The arithmetic mean is 675.

24 even divisors

2, 4, 8, 10, 14, 20, 28, 40, 56, 58, 70, 116, 140, 232, 280, 290, 406, 580, 812, 1160, 1624, 2030, 4060, 8120

8 odd divisors

1, 5, 7, 29, 35, 145, 203, 1015

How to compute the divisors of 8120?

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 8120 by each of the numbers from 1 to 8120 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)

8120 / 1 = 8120 (the remainder is 0, so 1 is a divisor of 8120)
8120 / 2 = 4060 (the remainder is 0, so 2 is a divisor of 8120)
8120 / 3 = 2706.6666666667 (the remainder is 2, so 3 is not a divisor of 8120)
...
8120 / 8119 = 1.0001231678778 (the remainder is 1, so 8119 is not a divisor of 8120)
8120 / 8120 = 1 (the remainder is 0, so 8120 is a divisor of 8120)

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 8120 (i.e. 90.11104260855). 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 $\frac{N}{d} = D$ )

8120 / 1 = 8120 (the remainder is 0, so 1 and 8120 are divisors of 8120)
8120 / 2 = 4060 (the remainder is 0, so 2 and 4060 are divisors of 8120)
8120 / 3 = 2706.6666666667 (the remainder is 2, so 3 is not a divisor of 8120)
...
8120 / 89 = 91.23595505618 (the remainder is 21, so 89 is not a divisor of 8120)
8120 / 90 = 90.222222222222 (the remainder is 20, so 90 is not a divisor of 8120)