What are the divisors of 9130?

1, 2, 5, 10, 11, 22, 55, 83, 110, 166, 415, 830, 913, 1826, 4565, 9130

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, 22, 110, 166, 830, 1826, 9130

8 odd divisors

1, 5, 11, 55, 83, 415, 913, 4565

How to compute the divisors of 9130?

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 9130 by each of the numbers from 1 to 9130 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)

9130 / 1 = 9130 (the remainder is 0, so 1 is a divisor of 9130)
9130 / 2 = 4565 (the remainder is 0, so 2 is a divisor of 9130)
9130 / 3 = 3043.3333333333 (the remainder is 1, so 3 is not a divisor of 9130)
...
9130 / 9129 = 1.0001095410231 (the remainder is 1, so 9129 is not a divisor of 9130)
9130 / 9130 = 1 (the remainder is 0, so 9130 is a divisor of 9130)

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 9130 (i.e. 95.55103348473). 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 $\frac{N}{d} = D$ )

9130 / 1 = 9130 (the remainder is 0, so 1 and 9130 are divisors of 9130)
9130 / 2 = 4565 (the remainder is 0, so 2 and 4565 are divisors of 9130)
9130 / 3 = 3043.3333333333 (the remainder is 1, so 3 is not a divisor of 9130)
...
9130 / 94 = 97.127659574468 (the remainder is 12, so 94 is not a divisor of 9130)
9130 / 95 = 96.105263157895 (the remainder is 10, so 95 is not a divisor of 9130)