What are the divisors of 8063?

1, 11, 733, 8063

There is a total of 4 positive divisors.
The sum of these divisors is 8808.
The arithmetic mean is 2202.

4 odd divisors

1, 11, 733, 8063

How to compute the divisors of 8063?

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 8063 by each of the numbers from 1 to 8063 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)

8063 / 1 = 8063 (the remainder is 0, so 1 is a divisor of 8063)
8063 / 2 = 4031.5 (the remainder is 1, so 2 is not a divisor of 8063)
8063 / 3 = 2687.6666666667 (the remainder is 2, so 3 is not a divisor of 8063)
...
8063 / 8062 = 1.0001240387001 (the remainder is 1, so 8062 is not a divisor of 8063)
8063 / 8063 = 1 (the remainder is 0, so 8063 is a divisor of 8063)

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 8063 (i.e. 89.794209167407). 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 $\frac{N}{d} = D$ )

8063 / 1 = 8063 (the remainder is 0, so 1 and 8063 are divisors of 8063)
8063 / 2 = 4031.5 (the remainder is 1, so 2 is not a divisor of 8063)
8063 / 3 = 2687.6666666667 (the remainder is 2, so 3 is not a divisor of 8063)
...
8063 / 88 = 91.625 (the remainder is 55, so 88 is not a divisor of 8063)
8063 / 89 = 90.595505617978 (the remainder is 53, so 89 is not a divisor of 8063)