What are the divisors of 8083?

1, 59, 137, 8083

There is a total of 4 positive divisors.
The sum of these divisors is 8280.
The arithmetic mean is 2070.

4 odd divisors

1, 59, 137, 8083

How to compute the divisors of 8083?

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 8083 by each of the numbers from 1 to 8083 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)

8083 / 1 = 8083 (the remainder is 0, so 1 is a divisor of 8083)
8083 / 2 = 4041.5 (the remainder is 1, so 2 is not a divisor of 8083)
8083 / 3 = 2694.3333333333 (the remainder is 1, so 3 is not a divisor of 8083)
...
8083 / 8082 = 1.0001237317496 (the remainder is 1, so 8082 is not a divisor of 8083)
8083 / 8083 = 1 (the remainder is 0, so 8083 is a divisor of 8083)

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 8083 (i.e. 89.905505949302). 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 $\frac{N}{d} = D$ )

8083 / 1 = 8083 (the remainder is 0, so 1 and 8083 are divisors of 8083)
8083 / 2 = 4041.5 (the remainder is 1, so 2 is not a divisor of 8083)
8083 / 3 = 2694.3333333333 (the remainder is 1, so 3 is not a divisor of 8083)
...
8083 / 88 = 91.852272727273 (the remainder is 75, so 88 is not a divisor of 8083)
8083 / 89 = 90.820224719101 (the remainder is 73, so 89 is not a divisor of 8083)