What are the divisors of 8049?

1, 3, 2683, 8049

There is a total of 4 positive divisors.
The sum of these divisors is 10736.
The arithmetic mean is 2684.

4 odd divisors

1, 3, 2683, 8049

How to compute the divisors of 8049?

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 8049 by each of the numbers from 1 to 8049 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)

8049 / 1 = 8049 (the remainder is 0, so 1 is a divisor of 8049)
8049 / 2 = 4024.5 (the remainder is 1, so 2 is not a divisor of 8049)
8049 / 3 = 2683 (the remainder is 0, so 3 is a divisor of 8049)
...
8049 / 8048 = 1.0001242544732 (the remainder is 1, so 8048 is not a divisor of 8049)
8049 / 8049 = 1 (the remainder is 0, so 8049 is a divisor of 8049)

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 8049 (i.e. 89.716219269428). 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 $\frac{N}{d} = D$ )

8049 / 1 = 8049 (the remainder is 0, so 1 and 8049 are divisors of 8049)
8049 / 2 = 4024.5 (the remainder is 1, so 2 is not a divisor of 8049)
8049 / 3 = 2683 (the remainder is 0, so 3 and 2683 are divisors of 8049)
...
8049 / 88 = 91.465909090909 (the remainder is 41, so 88 is not a divisor of 8049)
8049 / 89 = 90.438202247191 (the remainder is 39, so 89 is not a divisor of 8049)