What are the divisors of 8041?

1, 11, 17, 43, 187, 473, 731, 8041

There is a total of 8 positive divisors.
The sum of these divisors is 9504.
The arithmetic mean is 1188.

8 odd divisors

1, 11, 17, 43, 187, 473, 731, 8041

How to compute the divisors of 8041?

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 8041 by each of the numbers from 1 to 8041 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)

8041 / 1 = 8041 (the remainder is 0, so 1 is a divisor of 8041)
8041 / 2 = 4020.5 (the remainder is 1, so 2 is not a divisor of 8041)
8041 / 3 = 2680.3333333333 (the remainder is 1, so 3 is not a divisor of 8041)
...
8041 / 8040 = 1.0001243781095 (the remainder is 1, so 8040 is not a divisor of 8041)
8041 / 8041 = 1 (the remainder is 0, so 8041 is a divisor of 8041)

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 8041 (i.e. 89.671623159169). 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 $\frac{N}{d} = D$ )

8041 / 1 = 8041 (the remainder is 0, so 1 and 8041 are divisors of 8041)
8041 / 2 = 4020.5 (the remainder is 1, so 2 is not a divisor of 8041)
8041 / 3 = 2680.3333333333 (the remainder is 1, so 3 is not a divisor of 8041)
...
8041 / 88 = 91.375 (the remainder is 33, so 88 is not a divisor of 8041)
8041 / 89 = 90.348314606742 (the remainder is 31, so 89 is not a divisor of 8041)