What are the divisors of 8303?

1, 19, 23, 361, 437, 8303

There is a total of 6 positive divisors.
The sum of these divisors is 9144.
The arithmetic mean is 1524.

6 odd divisors

1, 19, 23, 361, 437, 8303

How to compute the divisors of 8303?

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 8303 by each of the numbers from 1 to 8303 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)

8303 / 1 = 8303 (the remainder is 0, so 1 is a divisor of 8303)
8303 / 2 = 4151.5 (the remainder is 1, so 2 is not a divisor of 8303)
8303 / 3 = 2767.6666666667 (the remainder is 2, so 3 is not a divisor of 8303)
...
8303 / 8302 = 1.0001204529029 (the remainder is 1, so 8302 is not a divisor of 8303)
8303 / 8303 = 1 (the remainder is 0, so 8303 is a divisor of 8303)

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 8303 (i.e. 91.120798942942). 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 $\frac{N}{d} = D$ )

8303 / 1 = 8303 (the remainder is 0, so 1 and 8303 are divisors of 8303)
8303 / 2 = 4151.5 (the remainder is 1, so 2 is not a divisor of 8303)
8303 / 3 = 2767.6666666667 (the remainder is 2, so 3 is not a divisor of 8303)
...
8303 / 90 = 92.255555555556 (the remainder is 23, so 90 is not a divisor of 8303)
8303 / 91 = 91.241758241758 (the remainder is 22, so 91 is not a divisor of 8303)