What are the divisors of 6008?

1, 2, 4, 8, 751, 1502, 3004, 6008

There is a total of 8 positive divisors.
The sum of these divisors is 11280.
The arithmetic mean is 1410.

6 even divisors

2, 4, 8, 1502, 3004, 6008

2 odd divisors

1, 751

How to compute the divisors of 6008?

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 6008 by each of the numbers from 1 to 6008 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)

6008 / 1 = 6008 (the remainder is 0, so 1 is a divisor of 6008)
6008 / 2 = 3004 (the remainder is 0, so 2 is a divisor of 6008)
6008 / 3 = 2002.6666666667 (the remainder is 2, so 3 is not a divisor of 6008)
...
6008 / 6007 = 1.0001664724488 (the remainder is 1, so 6007 is not a divisor of 6008)
6008 / 6008 = 1 (the remainder is 0, so 6008 is a divisor of 6008)

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 6008 (i.e. 77.511289500304). 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 $\frac{N}{d} = D$ )

6008 / 1 = 6008 (the remainder is 0, so 1 and 6008 are divisors of 6008)
6008 / 2 = 3004 (the remainder is 0, so 2 and 3004 are divisors of 6008)
6008 / 3 = 2002.6666666667 (the remainder is 2, so 3 is not a divisor of 6008)
...
6008 / 76 = 79.052631578947 (the remainder is 4, so 76 is not a divisor of 6008)
6008 / 77 = 78.025974025974 (the remainder is 2, so 77 is not a divisor of 6008)