What are the divisors of 8008?

1, 2, 4, 7, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 104, 143, 154, 182, 286, 308, 364, 572, 616, 728, 1001, 1144, 2002, 4004, 8008

There is a total of 32 positive divisors.
The sum of these divisors is 20160.
The arithmetic mean is 630.

24 even divisors

2, 4, 8, 14, 22, 26, 28, 44, 52, 56, 88, 104, 154, 182, 286, 308, 364, 572, 616, 728, 1144, 2002, 4004, 8008

8 odd divisors

1, 7, 11, 13, 77, 91, 143, 1001

How to compute the divisors of 8008?

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 8008 by each of the numbers from 1 to 8008 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)

8008 / 1 = 8008 (the remainder is 0, so 1 is a divisor of 8008)
8008 / 2 = 4004 (the remainder is 0, so 2 is a divisor of 8008)
8008 / 3 = 2669.3333333333 (the remainder is 1, so 3 is not a divisor of 8008)
...
8008 / 8007 = 1.0001248907206 (the remainder is 1, so 8007 is not a divisor of 8008)
8008 / 8008 = 1 (the remainder is 0, so 8008 is a divisor of 8008)

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 8008 (i.e. 89.487429284788). 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 $\frac{N}{d} = D$ )

8008 / 1 = 8008 (the remainder is 0, so 1 and 8008 are divisors of 8008)
8008 / 2 = 4004 (the remainder is 0, so 2 and 4004 are divisors of 8008)
8008 / 3 = 2669.3333333333 (the remainder is 1, so 3 is not a divisor of 8008)
...
8008 / 88 = 91 (the remainder is 0, so 88 and 91 are divisors of 8008)
8008 / 89 = 89.977528089888 (the remainder is 87, so 89 is not a divisor of 8008)