What are the divisors of 9137?

1, 9137

There is a total of 2 positive divisors.
The sum of these divisors is 9138.
The arithmetic mean is 4569.

2 odd divisors

1, 9137

How to compute the divisors of 9137?

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 9137 by each of the numbers from 1 to 9137 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)

9137 / 1 = 9137 (the remainder is 0, so 1 is a divisor of 9137)
9137 / 2 = 4568.5 (the remainder is 1, so 2 is not a divisor of 9137)
9137 / 3 = 3045.6666666667 (the remainder is 2, so 3 is not a divisor of 9137)
...
9137 / 9136 = 1.0001094570928 (the remainder is 1, so 9136 is not a divisor of 9137)
9137 / 9137 = 1 (the remainder is 0, so 9137 is a divisor of 9137)

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 9137 (i.e. 95.587656106843). 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 $\frac{N}{d} = D$ )

9137 / 1 = 9137 (the remainder is 0, so 1 and 9137 are divisors of 9137)
9137 / 2 = 4568.5 (the remainder is 1, so 2 is not a divisor of 9137)
9137 / 3 = 3045.6666666667 (the remainder is 2, so 3 is not a divisor of 9137)
...
9137 / 94 = 97.202127659574 (the remainder is 19, so 94 is not a divisor of 9137)
9137 / 95 = 96.178947368421 (the remainder is 17, so 95 is not a divisor of 9137)