What are the divisors of 8031?

1, 3, 2677, 8031

There is a total of 4 positive divisors.
The sum of these divisors is 10712.
The arithmetic mean is 2678.

4 odd divisors

1, 3, 2677, 8031

How to compute the divisors of 8031?

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 8031 by each of the numbers from 1 to 8031 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)

8031 / 1 = 8031 (the remainder is 0, so 1 is a divisor of 8031)
8031 / 2 = 4015.5 (the remainder is 1, so 2 is not a divisor of 8031)
8031 / 3 = 2677 (the remainder is 0, so 3 is a divisor of 8031)
...
8031 / 8030 = 1.0001245330012 (the remainder is 1, so 8030 is not a divisor of 8031)
8031 / 8031 = 1 (the remainder is 0, so 8031 is a divisor of 8031)

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 8031 (i.e. 89.615846812938). 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 $\frac{N}{d} = D$ )

8031 / 1 = 8031 (the remainder is 0, so 1 and 8031 are divisors of 8031)
8031 / 2 = 4015.5 (the remainder is 1, so 2 is not a divisor of 8031)
8031 / 3 = 2677 (the remainder is 0, so 3 and 2677 are divisors of 8031)
...
8031 / 88 = 91.261363636364 (the remainder is 23, so 88 is not a divisor of 8031)
8031 / 89 = 90.23595505618 (the remainder is 21, so 89 is not a divisor of 8031)