What are the divisors of 9014?

1, 2, 4507, 9014

There is a total of 4 positive divisors.
The sum of these divisors is 13524.
The arithmetic mean is 3381.

2 even divisors

2, 9014

2 odd divisors

1, 4507

How to compute the divisors of 9014?

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 9014 by each of the numbers from 1 to 9014 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)

9014 / 1 = 9014 (the remainder is 0, so 1 is a divisor of 9014)
9014 / 2 = 4507 (the remainder is 0, so 2 is a divisor of 9014)
9014 / 3 = 3004.6666666667 (the remainder is 2, so 3 is not a divisor of 9014)
...
9014 / 9013 = 1.0001109508488 (the remainder is 1, so 9013 is not a divisor of 9014)
9014 / 9014 = 1 (the remainder is 0, so 9014 is a divisor of 9014)

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 9014 (i.e. 94.942087611343). 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 $\frac{N}{d} = D$ )

9014 / 1 = 9014 (the remainder is 0, so 1 and 9014 are divisors of 9014)
9014 / 2 = 4507 (the remainder is 0, so 2 and 4507 are divisors of 9014)
9014 / 3 = 3004.6666666667 (the remainder is 2, so 3 is not a divisor of 9014)
...
9014 / 93 = 96.924731182796 (the remainder is 86, so 93 is not a divisor of 9014)
9014 / 94 = 95.893617021277 (the remainder is 84, so 94 is not a divisor of 9014)