What are the divisors of 8060?

1, 2, 4, 5, 10, 13, 20, 26, 31, 52, 62, 65, 124, 130, 155, 260, 310, 403, 620, 806, 1612, 2015, 4030, 8060

There is a total of 24 positive divisors.
The sum of these divisors is 18816.
The arithmetic mean is 784.

16 even divisors

2, 4, 10, 20, 26, 52, 62, 124, 130, 260, 310, 620, 806, 1612, 4030, 8060

8 odd divisors

1, 5, 13, 31, 65, 155, 403, 2015

How to compute the divisors of 8060?

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 8060 by each of the numbers from 1 to 8060 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)

8060 / 1 = 8060 (the remainder is 0, so 1 is a divisor of 8060)
8060 / 2 = 4030 (the remainder is 0, so 2 is a divisor of 8060)
8060 / 3 = 2686.6666666667 (the remainder is 2, so 3 is not a divisor of 8060)
...
8060 / 8059 = 1.0001240848741 (the remainder is 1, so 8059 is not a divisor of 8060)
8060 / 8060 = 1 (the remainder is 0, so 8060 is a divisor of 8060)

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 8060 (i.e. 89.777502749854). 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 $\frac{N}{d} = D$ )

8060 / 1 = 8060 (the remainder is 0, so 1 and 8060 are divisors of 8060)
8060 / 2 = 4030 (the remainder is 0, so 2 and 4030 are divisors of 8060)
8060 / 3 = 2686.6666666667 (the remainder is 2, so 3 is not a divisor of 8060)
...
8060 / 88 = 91.590909090909 (the remainder is 52, so 88 is not a divisor of 8060)
8060 / 89 = 90.561797752809 (the remainder is 50, so 89 is not a divisor of 8060)