What are the divisors of 9111?

1, 3, 3037, 9111

There is a total of 4 positive divisors.
The sum of these divisors is 12152.
The arithmetic mean is 3038.

4 odd divisors

1, 3, 3037, 9111

How to compute the divisors of 9111?

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 9111 by each of the numbers from 1 to 9111 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)

9111 / 1 = 9111 (the remainder is 0, so 1 is a divisor of 9111)
9111 / 2 = 4555.5 (the remainder is 1, so 2 is not a divisor of 9111)
9111 / 3 = 3037 (the remainder is 0, so 3 is a divisor of 9111)
...
9111 / 9110 = 1.0001097694841 (the remainder is 1, so 9110 is not a divisor of 9111)
9111 / 9111 = 1 (the remainder is 0, so 9111 is a divisor of 9111)

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 9111 (i.e. 95.451558394821). 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 $\frac{N}{d} = D$ )

9111 / 1 = 9111 (the remainder is 0, so 1 and 9111 are divisors of 9111)
9111 / 2 = 4555.5 (the remainder is 1, so 2 is not a divisor of 9111)
9111 / 3 = 3037 (the remainder is 0, so 3 and 3037 are divisors of 9111)
...
9111 / 94 = 96.925531914894 (the remainder is 87, so 94 is not a divisor of 9111)
9111 / 95 = 95.905263157895 (the remainder is 86, so 95 is not a divisor of 9111)