What are the divisors of 9181?

1, 9181

There is a total of 2 positive divisors.
The sum of these divisors is 9182.
The arithmetic mean is 4591.

2 odd divisors

1, 9181

How to compute the divisors of 9181?

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 9181 by each of the numbers from 1 to 9181 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)

9181 / 1 = 9181 (the remainder is 0, so 1 is a divisor of 9181)
9181 / 2 = 4590.5 (the remainder is 1, so 2 is not a divisor of 9181)
9181 / 3 = 3060.3333333333 (the remainder is 1, so 3 is not a divisor of 9181)
...
9181 / 9180 = 1.0001089324619 (the remainder is 1, so 9180 is not a divisor of 9181)
9181 / 9181 = 1 (the remainder is 0, so 9181 is a divisor of 9181)

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 9181 (i.e. 95.817534929678). 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 $\frac{N}{d} = D$ )

9181 / 1 = 9181 (the remainder is 0, so 1 and 9181 are divisors of 9181)
9181 / 2 = 4590.5 (the remainder is 1, so 2 is not a divisor of 9181)
9181 / 3 = 3060.3333333333 (the remainder is 1, so 3 is not a divisor of 9181)
...
9181 / 94 = 97.670212765957 (the remainder is 63, so 94 is not a divisor of 9181)
9181 / 95 = 96.642105263158 (the remainder is 61, so 95 is not a divisor of 9181)