What are the divisors of 9004?

1, 2, 4, 2251, 4502, 9004

There is a total of 6 positive divisors.
The sum of these divisors is 15764.
The arithmetic mean is 2627.3333333333.

4 even divisors

2, 4, 4502, 9004

2 odd divisors

1, 2251

How to compute the divisors of 9004?

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 9004 by each of the numbers from 1 to 9004 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)

9004 / 1 = 9004 (the remainder is 0, so 1 is a divisor of 9004)
9004 / 2 = 4502 (the remainder is 0, so 2 is a divisor of 9004)
9004 / 3 = 3001.3333333333 (the remainder is 1, so 3 is not a divisor of 9004)
...
9004 / 9003 = 1.0001110740864 (the remainder is 1, so 9003 is not a divisor of 9004)
9004 / 9004 = 1 (the remainder is 0, so 9004 is a divisor of 9004)

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 9004 (i.e. 94.889409314212). 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 $\frac{N}{d} = D$ )

9004 / 1 = 9004 (the remainder is 0, so 1 and 9004 are divisors of 9004)
9004 / 2 = 4502 (the remainder is 0, so 2 and 4502 are divisors of 9004)
9004 / 3 = 3001.3333333333 (the remainder is 1, so 3 is not a divisor of 9004)
...
9004 / 93 = 96.817204301075 (the remainder is 76, so 93 is not a divisor of 9004)
9004 / 94 = 95.787234042553 (the remainder is 74, so 94 is not a divisor of 9004)