What are the divisors of 8234?

1, 2, 23, 46, 179, 358, 4117, 8234

There is a total of 8 positive divisors.
The sum of these divisors is 12960.
The arithmetic mean is 1620.

4 even divisors

2, 46, 358, 8234

4 odd divisors

1, 23, 179, 4117

How to compute the divisors of 8234?

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 8234 by each of the numbers from 1 to 8234 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)

8234 / 1 = 8234 (the remainder is 0, so 1 is a divisor of 8234)
8234 / 2 = 4117 (the remainder is 0, so 2 is a divisor of 8234)
8234 / 3 = 2744.6666666667 (the remainder is 2, so 3 is not a divisor of 8234)
...
8234 / 8233 = 1.0001214624074 (the remainder is 1, so 8233 is not a divisor of 8234)
8234 / 8234 = 1 (the remainder is 0, so 8234 is a divisor of 8234)

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 8234 (i.e. 90.741390776205). 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 $\frac{N}{d} = D$ )

8234 / 1 = 8234 (the remainder is 0, so 1 and 8234 are divisors of 8234)
8234 / 2 = 4117 (the remainder is 0, so 2 and 4117 are divisors of 8234)
8234 / 3 = 2744.6666666667 (the remainder is 2, so 3 is not a divisor of 8234)
...
8234 / 89 = 92.516853932584 (the remainder is 46, so 89 is not a divisor of 8234)
8234 / 90 = 91.488888888889 (the remainder is 44, so 90 is not a divisor of 8234)