What are the divisors of 8030?

1, 2, 5, 10, 11, 22, 55, 73, 110, 146, 365, 730, 803, 1606, 4015, 8030

There is a total of 16 positive divisors.
The sum of these divisors is 15984.
The arithmetic mean is 999.

8 even divisors

2, 10, 22, 110, 146, 730, 1606, 8030

8 odd divisors

1, 5, 11, 55, 73, 365, 803, 4015

How to compute the divisors of 8030?

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 8030 by each of the numbers from 1 to 8030 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)

8030 / 1 = 8030 (the remainder is 0, so 1 is a divisor of 8030)
8030 / 2 = 4015 (the remainder is 0, so 2 is a divisor of 8030)
8030 / 3 = 2676.6666666667 (the remainder is 2, so 3 is not a divisor of 8030)
...
8030 / 8029 = 1.0001245485116 (the remainder is 1, so 8029 is not a divisor of 8030)
8030 / 8030 = 1 (the remainder is 0, so 8030 is a divisor of 8030)

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 8030 (i.e. 89.610267268879). 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 $\frac{N}{d} = D$ )

8030 / 1 = 8030 (the remainder is 0, so 1 and 8030 are divisors of 8030)
8030 / 2 = 4015 (the remainder is 0, so 2 and 4015 are divisors of 8030)
8030 / 3 = 2676.6666666667 (the remainder is 2, so 3 is not a divisor of 8030)
...
8030 / 88 = 91.25 (the remainder is 22, so 88 is not a divisor of 8030)
8030 / 89 = 90.224719101124 (the remainder is 20, so 89 is not a divisor of 8030)