What are the divisors of 8223?

1, 3, 2741, 8223

There is a total of 4 positive divisors.
The sum of these divisors is 10968.
The arithmetic mean is 2742.

4 odd divisors

1, 3, 2741, 8223

How to compute the divisors of 8223?

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 8223 by each of the numbers from 1 to 8223 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)

8223 / 1 = 8223 (the remainder is 0, so 1 is a divisor of 8223)
8223 / 2 = 4111.5 (the remainder is 1, so 2 is not a divisor of 8223)
8223 / 3 = 2741 (the remainder is 0, so 3 is a divisor of 8223)
...
8223 / 8222 = 1.0001216249088 (the remainder is 1, so 8222 is not a divisor of 8223)
8223 / 8223 = 1 (the remainder is 0, so 8223 is a divisor of 8223)

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 8223 (i.e. 90.68075870878). 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 $\frac{N}{d} = D$ )

8223 / 1 = 8223 (the remainder is 0, so 1 and 8223 are divisors of 8223)
8223 / 2 = 4111.5 (the remainder is 1, so 2 is not a divisor of 8223)
8223 / 3 = 2741 (the remainder is 0, so 3 and 2741 are divisors of 8223)
...
8223 / 89 = 92.393258426966 (the remainder is 35, so 89 is not a divisor of 8223)
8223 / 90 = 91.366666666667 (the remainder is 33, so 90 is not a divisor of 8223)