What are the divisors of 8290?

1, 2, 5, 10, 829, 1658, 4145, 8290

There is a total of 8 positive divisors.
The sum of these divisors is 14940.
The arithmetic mean is 1867.5.

4 even divisors

2, 10, 1658, 8290

4 odd divisors

1, 5, 829, 4145

How to compute the divisors of 8290?

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 8290 by each of the numbers from 1 to 8290 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)

8290 / 1 = 8290 (the remainder is 0, so 1 is a divisor of 8290)
8290 / 2 = 4145 (the remainder is 0, so 2 is a divisor of 8290)
8290 / 3 = 2763.3333333333 (the remainder is 1, so 3 is not a divisor of 8290)
...
8290 / 8289 = 1.0001206418145 (the remainder is 1, so 8289 is not a divisor of 8290)
8290 / 8290 = 1 (the remainder is 0, so 8290 is a divisor of 8290)

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 8290 (i.e. 91.04943712072). 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 $\frac{N}{d} = D$ )

8290 / 1 = 8290 (the remainder is 0, so 1 and 8290 are divisors of 8290)
8290 / 2 = 4145 (the remainder is 0, so 2 and 4145 are divisors of 8290)
8290 / 3 = 2763.3333333333 (the remainder is 1, so 3 is not a divisor of 8290)
...
8290 / 90 = 92.111111111111 (the remainder is 10, so 90 is not a divisor of 8290)
8290 / 91 = 91.098901098901 (the remainder is 9, so 91 is not a divisor of 8290)