What are the divisors of 9071?

1, 47, 193, 9071

There is a total of 4 positive divisors.
The sum of these divisors is 9312.
The arithmetic mean is 2328.

4 odd divisors

1, 47, 193, 9071

How to compute the divisors of 9071?

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 9071 by each of the numbers from 1 to 9071 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)

9071 / 1 = 9071 (the remainder is 0, so 1 is a divisor of 9071)
9071 / 2 = 4535.5 (the remainder is 1, so 2 is not a divisor of 9071)
9071 / 3 = 3023.6666666667 (the remainder is 2, so 3 is not a divisor of 9071)
...
9071 / 9070 = 1.0001102535832 (the remainder is 1, so 9070 is not a divisor of 9071)
9071 / 9071 = 1 (the remainder is 0, so 9071 is a divisor of 9071)

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 9071 (i.e. 95.241797547085). 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 $\frac{N}{d} = D$ )

9071 / 1 = 9071 (the remainder is 0, so 1 and 9071 are divisors of 9071)
9071 / 2 = 4535.5 (the remainder is 1, so 2 is not a divisor of 9071)
9071 / 3 = 3023.6666666667 (the remainder is 2, so 3 is not a divisor of 9071)
...
9071 / 94 = 96.5 (the remainder is 47, so 94 is not a divisor of 9071)
9071 / 95 = 95.484210526316 (the remainder is 46, so 95 is not a divisor of 9071)