What are the divisors of 8043?

1, 3, 7, 21, 383, 1149, 2681, 8043

There is a total of 8 positive divisors.
The sum of these divisors is 12288.
The arithmetic mean is 1536.

8 odd divisors

1, 3, 7, 21, 383, 1149, 2681, 8043

How to compute the divisors of 8043?

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 8043 by each of the numbers from 1 to 8043 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)

8043 / 1 = 8043 (the remainder is 0, so 1 is a divisor of 8043)
8043 / 2 = 4021.5 (the remainder is 1, so 2 is not a divisor of 8043)
8043 / 3 = 2681 (the remainder is 0, so 3 is a divisor of 8043)
...
8043 / 8042 = 1.0001243471773 (the remainder is 1, so 8042 is not a divisor of 8043)
8043 / 8043 = 1 (the remainder is 0, so 8043 is a divisor of 8043)

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 8043 (i.e. 89.682774265742). 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 $\frac{N}{d} = D$ )

8043 / 1 = 8043 (the remainder is 0, so 1 and 8043 are divisors of 8043)
8043 / 2 = 4021.5 (the remainder is 1, so 2 is not a divisor of 8043)
8043 / 3 = 2681 (the remainder is 0, so 3 and 2681 are divisors of 8043)
...
8043 / 88 = 91.397727272727 (the remainder is 35, so 88 is not a divisor of 8043)
8043 / 89 = 90.370786516854 (the remainder is 33, so 89 is not a divisor of 8043)