What are the divisors of 9013?

1, 9013

There is a total of 2 positive divisors.
The sum of these divisors is 9014.
The arithmetic mean is 4507.

2 odd divisors

1, 9013

How to compute the divisors of 9013?

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 9013 by each of the numbers from 1 to 9013 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)

9013 / 1 = 9013 (the remainder is 0, so 1 is a divisor of 9013)
9013 / 2 = 4506.5 (the remainder is 1, so 2 is not a divisor of 9013)
9013 / 3 = 3004.3333333333 (the remainder is 1, so 3 is not a divisor of 9013)
...
9013 / 9012 = 1.0001109631602 (the remainder is 1, so 9012 is not a divisor of 9013)
9013 / 9013 = 1 (the remainder is 0, so 9013 is a divisor of 9013)

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 9013 (i.e. 94.93682109698). 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 $\frac{N}{d} = D$ )

9013 / 1 = 9013 (the remainder is 0, so 1 and 9013 are divisors of 9013)
9013 / 2 = 4506.5 (the remainder is 1, so 2 is not a divisor of 9013)
9013 / 3 = 3004.3333333333 (the remainder is 1, so 3 is not a divisor of 9013)
...
9013 / 93 = 96.913978494624 (the remainder is 85, so 93 is not a divisor of 9013)
9013 / 94 = 95.882978723404 (the remainder is 83, so 94 is not a divisor of 9013)