What are the divisors of 9163?

1, 7, 11, 17, 49, 77, 119, 187, 539, 833, 1309, 9163

There is a total of 12 positive divisors.
The sum of these divisors is 12312.
The arithmetic mean is 1026.

12 odd divisors

1, 7, 11, 17, 49, 77, 119, 187, 539, 833, 1309, 9163

How to compute the divisors of 9163?

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 9163 by each of the numbers from 1 to 9163 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)

9163 / 1 = 9163 (the remainder is 0, so 1 is a divisor of 9163)
9163 / 2 = 4581.5 (the remainder is 1, so 2 is not a divisor of 9163)
9163 / 3 = 3054.3333333333 (the remainder is 1, so 3 is not a divisor of 9163)
...
9163 / 9162 = 1.0001091464746 (the remainder is 1, so 9162 is not a divisor of 9163)
9163 / 9163 = 1 (the remainder is 0, so 9163 is a divisor of 9163)

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 9163 (i.e. 95.723560318241). 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 $\frac{N}{d} = D$ )

9163 / 1 = 9163 (the remainder is 0, so 1 and 9163 are divisors of 9163)
9163 / 2 = 4581.5 (the remainder is 1, so 2 is not a divisor of 9163)
9163 / 3 = 3054.3333333333 (the remainder is 1, so 3 is not a divisor of 9163)
...
9163 / 94 = 97.478723404255 (the remainder is 45, so 94 is not a divisor of 9163)
9163 / 95 = 96.452631578947 (the remainder is 43, so 95 is not a divisor of 9163)