What are the divisors of 9167?

1, 89, 103, 9167

There is a total of 4 positive divisors.
The sum of these divisors is 9360.
The arithmetic mean is 2340.

4 odd divisors

1, 89, 103, 9167

How to compute the divisors of 9167?

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 9167 by each of the numbers from 1 to 9167 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)

9167 / 1 = 9167 (the remainder is 0, so 1 is a divisor of 9167)
9167 / 2 = 4583.5 (the remainder is 1, so 2 is not a divisor of 9167)
9167 / 3 = 3055.6666666667 (the remainder is 2, so 3 is not a divisor of 9167)
...
9167 / 9166 = 1.0001090988436 (the remainder is 1, so 9166 is not a divisor of 9167)
9167 / 9167 = 1 (the remainder is 0, so 9167 is a divisor of 9167)

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 9167 (i.e. 95.744451536368). 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 $\frac{N}{d} = D$ )

9167 / 1 = 9167 (the remainder is 0, so 1 and 9167 are divisors of 9167)
9167 / 2 = 4583.5 (the remainder is 1, so 2 is not a divisor of 9167)
9167 / 3 = 3055.6666666667 (the remainder is 2, so 3 is not a divisor of 9167)
...
9167 / 94 = 97.521276595745 (the remainder is 49, so 94 is not a divisor of 9167)
9167 / 95 = 96.494736842105 (the remainder is 47, so 95 is not a divisor of 9167)