What are the divisors of 9230?

1, 2, 5, 10, 13, 26, 65, 71, 130, 142, 355, 710, 923, 1846, 4615, 9230

There is a total of 16 positive divisors.
The sum of these divisors is 18144.
The arithmetic mean is 1134.

8 even divisors

2, 10, 26, 130, 142, 710, 1846, 9230

8 odd divisors

1, 5, 13, 65, 71, 355, 923, 4615

How to compute the divisors of 9230?

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 9230 by each of the numbers from 1 to 9230 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)

9230 / 1 = 9230 (the remainder is 0, so 1 is a divisor of 9230)
9230 / 2 = 4615 (the remainder is 0, so 2 is a divisor of 9230)
9230 / 3 = 3076.6666666667 (the remainder is 2, so 3 is not a divisor of 9230)
...
9230 / 9229 = 1.0001083541012 (the remainder is 1, so 9229 is not a divisor of 9230)
9230 / 9230 = 1 (the remainder is 0, so 9230 is a divisor of 9230)

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 9230 (i.e. 96.072888995804). 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 $\frac{N}{d} = D$ )

9230 / 1 = 9230 (the remainder is 0, so 1 and 9230 are divisors of 9230)
9230 / 2 = 4615 (the remainder is 0, so 2 and 4615 are divisors of 9230)
9230 / 3 = 3076.6666666667 (the remainder is 2, so 3 is not a divisor of 9230)
...
9230 / 95 = 97.157894736842 (the remainder is 15, so 95 is not a divisor of 9230)
9230 / 96 = 96.145833333333 (the remainder is 14, so 96 is not a divisor of 9230)