What are the divisors of 8229?

1, 3, 13, 39, 211, 633, 2743, 8229

There is a total of 8 positive divisors.
The sum of these divisors is 11872.
The arithmetic mean is 1484.

8 odd divisors

1, 3, 13, 39, 211, 633, 2743, 8229

How to compute the divisors of 8229?

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 8229 by each of the numbers from 1 to 8229 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)

8229 / 1 = 8229 (the remainder is 0, so 1 is a divisor of 8229)
8229 / 2 = 4114.5 (the remainder is 1, so 2 is not a divisor of 8229)
8229 / 3 = 2743 (the remainder is 0, so 3 is a divisor of 8229)
...
8229 / 8228 = 1.0001215362178 (the remainder is 1, so 8228 is not a divisor of 8229)
8229 / 8229 = 1 (the remainder is 0, so 8229 is a divisor of 8229)

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 8229 (i.e. 90.713835769413). 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 $\frac{N}{d} = D$ )

8229 / 1 = 8229 (the remainder is 0, so 1 and 8229 are divisors of 8229)
8229 / 2 = 4114.5 (the remainder is 1, so 2 is not a divisor of 8229)
8229 / 3 = 2743 (the remainder is 0, so 3 and 2743 are divisors of 8229)
...
8229 / 89 = 92.460674157303 (the remainder is 41, so 89 is not a divisor of 8229)
8229 / 90 = 91.433333333333 (the remainder is 39, so 90 is not a divisor of 8229)