What are the divisors of 5008?

1, 2, 4, 8, 16, 313, 626, 1252, 2504, 5008

There is a total of 10 positive divisors.
The sum of these divisors is 9734.
The arithmetic mean is 973.4.

8 even divisors

2, 4, 8, 16, 626, 1252, 2504, 5008

2 odd divisors

1, 313

How to compute the divisors of 5008?

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 5008 by each of the numbers from 1 to 5008 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)

5008 / 1 = 5008 (the remainder is 0, so 1 is a divisor of 5008)
5008 / 2 = 2504 (the remainder is 0, so 2 is a divisor of 5008)
5008 / 3 = 1669.3333333333 (the remainder is 1, so 3 is not a divisor of 5008)
...
5008 / 5007 = 1.0001997203915 (the remainder is 1, so 5007 is not a divisor of 5008)
5008 / 5008 = 1 (the remainder is 0, so 5008 is a divisor of 5008)

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 5008 (i.e. 70.767224051817). 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 $\frac{N}{d} = D$ )

5008 / 1 = 5008 (the remainder is 0, so 1 and 5008 are divisors of 5008)
5008 / 2 = 2504 (the remainder is 0, so 2 and 2504 are divisors of 5008)
5008 / 3 = 1669.3333333333 (the remainder is 1, so 3 is not a divisor of 5008)
...
5008 / 69 = 72.579710144928 (the remainder is 40, so 69 is not a divisor of 5008)
5008 / 70 = 71.542857142857 (the remainder is 38, so 70 is not a divisor of 5008)