What are the divisors of 8203?

1, 13, 631, 8203

There is a total of 4 positive divisors.
The sum of these divisors is 8848.
The arithmetic mean is 2212.

4 odd divisors

1, 13, 631, 8203

How to compute the divisors of 8203?

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 8203 by each of the numbers from 1 to 8203 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)

8203 / 1 = 8203 (the remainder is 0, so 1 is a divisor of 8203)
8203 / 2 = 4101.5 (the remainder is 1, so 2 is not a divisor of 8203)
8203 / 3 = 2734.3333333333 (the remainder is 1, so 3 is not a divisor of 8203)
...
8203 / 8202 = 1.0001219214826 (the remainder is 1, so 8202 is not a divisor of 8203)
8203 / 8203 = 1 (the remainder is 0, so 8203 is a divisor of 8203)

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 8203 (i.e. 90.570414595496). 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 $\frac{N}{d} = D$ )

8203 / 1 = 8203 (the remainder is 0, so 1 and 8203 are divisors of 8203)
8203 / 2 = 4101.5 (the remainder is 1, so 2 is not a divisor of 8203)
8203 / 3 = 2734.3333333333 (the remainder is 1, so 3 is not a divisor of 8203)
...
8203 / 89 = 92.168539325843 (the remainder is 15, so 89 is not a divisor of 8203)
8203 / 90 = 91.144444444444 (the remainder is 13, so 90 is not a divisor of 8203)