What are the divisors of 9011?

1, 9011

There is a total of 2 positive divisors.
The sum of these divisors is 9012.
The arithmetic mean is 4506.

2 odd divisors

1, 9011

How to compute the divisors of 9011?

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 9011 by each of the numbers from 1 to 9011 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)

9011 / 1 = 9011 (the remainder is 0, so 1 is a divisor of 9011)
9011 / 2 = 4505.5 (the remainder is 1, so 2 is not a divisor of 9011)
9011 / 3 = 3003.6666666667 (the remainder is 2, so 3 is not a divisor of 9011)
...
9011 / 9010 = 1.0001109877913 (the remainder is 1, so 9010 is not a divisor of 9011)
9011 / 9011 = 1 (the remainder is 0, so 9011 is a divisor of 9011)

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 9011 (i.e. 94.926287191694). 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 $\frac{N}{d} = D$ )

9011 / 1 = 9011 (the remainder is 0, so 1 and 9011 are divisors of 9011)
9011 / 2 = 4505.5 (the remainder is 1, so 2 is not a divisor of 9011)
9011 / 3 = 3003.6666666667 (the remainder is 2, so 3 is not a divisor of 9011)
...
9011 / 93 = 96.89247311828 (the remainder is 83, so 93 is not a divisor of 9011)
9011 / 94 = 95.86170212766 (the remainder is 81, so 94 is not a divisor of 9011)