What are the divisors of 9008?

1, 2, 4, 8, 16, 563, 1126, 2252, 4504, 9008

There is a total of 10 positive divisors.
The sum of these divisors is 17484.
The arithmetic mean is 1748.4.

8 even divisors

2, 4, 8, 16, 1126, 2252, 4504, 9008

2 odd divisors

1, 563

How to compute the divisors of 9008?

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 9008 by each of the numbers from 1 to 9008 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)

9008 / 1 = 9008 (the remainder is 0, so 1 is a divisor of 9008)
9008 / 2 = 4504 (the remainder is 0, so 2 is a divisor of 9008)
9008 / 3 = 3002.6666666667 (the remainder is 2, so 3 is not a divisor of 9008)
...
9008 / 9007 = 1.0001110247585 (the remainder is 1, so 9007 is not a divisor of 9008)
9008 / 9008 = 1 (the remainder is 0, so 9008 is a divisor of 9008)

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 9008 (i.e. 94.910484141637). 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 $\frac{N}{d} = D$ )

9008 / 1 = 9008 (the remainder is 0, so 1 and 9008 are divisors of 9008)
9008 / 2 = 4504 (the remainder is 0, so 2 and 4504 are divisors of 9008)
9008 / 3 = 3002.6666666667 (the remainder is 2, so 3 is not a divisor of 9008)
...
9008 / 93 = 96.860215053763 (the remainder is 80, so 93 is not a divisor of 9008)
9008 / 94 = 95.829787234043 (the remainder is 78, so 94 is not a divisor of 9008)