What are the divisors of 6004?

1, 2, 4, 19, 38, 76, 79, 158, 316, 1501, 3002, 6004

There is a total of 12 positive divisors.
The sum of these divisors is 11200.
The arithmetic mean is 933.33333333333.

8 even divisors

2, 4, 38, 76, 158, 316, 3002, 6004

4 odd divisors

1, 19, 79, 1501

How to compute the divisors of 6004?

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 6004 by each of the numbers from 1 to 6004 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)

6004 / 1 = 6004 (the remainder is 0, so 1 is a divisor of 6004)
6004 / 2 = 3002 (the remainder is 0, so 2 is a divisor of 6004)
6004 / 3 = 2001.3333333333 (the remainder is 1, so 3 is not a divisor of 6004)
...
6004 / 6003 = 1.000166583375 (the remainder is 1, so 6003 is not a divisor of 6004)
6004 / 6004 = 1 (the remainder is 0, so 6004 is a divisor of 6004)

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 6004 (i.e. 77.485482511242). 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 $\frac{N}{d} = D$ )

6004 / 1 = 6004 (the remainder is 0, so 1 and 6004 are divisors of 6004)
6004 / 2 = 3002 (the remainder is 0, so 2 and 3002 are divisors of 6004)
6004 / 3 = 2001.3333333333 (the remainder is 1, so 3 is not a divisor of 6004)
...
6004 / 76 = 79 (the remainder is 0, so 76 and 79 are divisors of 6004)
6004 / 77 = 77.974025974026 (the remainder is 75, so 77 is not a divisor of 6004)