What are the divisors of 9129?

1, 3, 17, 51, 179, 537, 3043, 9129

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

8 odd divisors

1, 3, 17, 51, 179, 537, 3043, 9129

How to compute the divisors of 9129?

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 9129 by each of the numbers from 1 to 9129 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)

9129 / 1 = 9129 (the remainder is 0, so 1 is a divisor of 9129)
9129 / 2 = 4564.5 (the remainder is 1, so 2 is not a divisor of 9129)
9129 / 3 = 3043 (the remainder is 0, so 3 is a divisor of 9129)
...
9129 / 9128 = 1.0001095530237 (the remainder is 1, so 9128 is not a divisor of 9129)
9129 / 9129 = 1 (the remainder is 0, so 9129 is a divisor of 9129)

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 9129 (i.e. 95.545800535659). 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 $\frac{N}{d} = D$ )

9129 / 1 = 9129 (the remainder is 0, so 1 and 9129 are divisors of 9129)
9129 / 2 = 4564.5 (the remainder is 1, so 2 is not a divisor of 9129)
9129 / 3 = 3043 (the remainder is 0, so 3 and 3043 are divisors of 9129)
...
9129 / 94 = 97.117021276596 (the remainder is 11, so 94 is not a divisor of 9129)
9129 / 95 = 96.094736842105 (the remainder is 9, so 95 is not a divisor of 9129)