What are the divisors of 8045?

1, 5, 1609, 8045

There is a total of 4 positive divisors.
The sum of these divisors is 9660.
The arithmetic mean is 2415.

4 odd divisors

1, 5, 1609, 8045

How to compute the divisors of 8045?

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 8045 by each of the numbers from 1 to 8045 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)

8045 / 1 = 8045 (the remainder is 0, so 1 is a divisor of 8045)
8045 / 2 = 4022.5 (the remainder is 1, so 2 is not a divisor of 8045)
8045 / 3 = 2681.6666666667 (the remainder is 2, so 3 is not a divisor of 8045)
...
8045 / 8044 = 1.0001243162606 (the remainder is 1, so 8044 is not a divisor of 8045)
8045 / 8045 = 1 (the remainder is 0, so 8045 is a divisor of 8045)

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 8045 (i.e. 89.693923985965). 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 $\frac{N}{d} = D$ )

8045 / 1 = 8045 (the remainder is 0, so 1 and 8045 are divisors of 8045)
8045 / 2 = 4022.5 (the remainder is 1, so 2 is not a divisor of 8045)
8045 / 3 = 2681.6666666667 (the remainder is 2, so 3 is not a divisor of 8045)
...
8045 / 88 = 91.420454545455 (the remainder is 37, so 88 is not a divisor of 8045)
8045 / 89 = 90.393258426966 (the remainder is 35, so 89 is not a divisor of 8045)