What are the divisors of 9127?

1, 9127

There is a total of 2 positive divisors.
The sum of these divisors is 9128.
The arithmetic mean is 4564.

2 odd divisors

1, 9127

How to compute the divisors of 9127?

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 9127 by each of the numbers from 1 to 9127 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)

9127 / 1 = 9127 (the remainder is 0, so 1 is a divisor of 9127)
9127 / 2 = 4563.5 (the remainder is 1, so 2 is not a divisor of 9127)
9127 / 3 = 3042.3333333333 (the remainder is 1, so 3 is not a divisor of 9127)
...
9127 / 9126 = 1.0001095770327 (the remainder is 1, so 9126 is not a divisor of 9127)
9127 / 9127 = 1 (the remainder is 0, so 9127 is a divisor of 9127)

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 9127 (i.e. 95.535333777613). 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 $\frac{N}{d} = D$ )

9127 / 1 = 9127 (the remainder is 0, so 1 and 9127 are divisors of 9127)
9127 / 2 = 4563.5 (the remainder is 1, so 2 is not a divisor of 9127)
9127 / 3 = 3042.3333333333 (the remainder is 1, so 3 is not a divisor of 9127)
...
9127 / 94 = 97.095744680851 (the remainder is 9, so 94 is not a divisor of 9127)
9127 / 95 = 96.073684210526 (the remainder is 7, so 95 is not a divisor of 9127)