What are the divisors of 3004?

1, 2, 4, 751, 1502, 3004

There is a total of 6 positive divisors.
The sum of these divisors is 5264.
The arithmetic mean is 877.33333333333.

4 even divisors

2, 4, 1502, 3004

2 odd divisors

1, 751

How to compute the divisors of 3004?

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 3004 by each of the numbers from 1 to 3004 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)

3004 / 1 = 3004 (the remainder is 0, so 1 is a divisor of 3004)
3004 / 2 = 1502 (the remainder is 0, so 2 is a divisor of 3004)
3004 / 3 = 1001.3333333333 (the remainder is 1, so 3 is not a divisor of 3004)
...
3004 / 3003 = 1.000333000333 (the remainder is 1, so 3003 is not a divisor of 3004)
3004 / 3004 = 1 (the remainder is 0, so 3004 is a divisor of 3004)

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 3004 (i.e. 54.808758424179). 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 $\frac{N}{d} = D$ )

3004 / 1 = 3004 (the remainder is 0, so 1 and 3004 are divisors of 3004)
3004 / 2 = 1502 (the remainder is 0, so 2 and 1502 are divisors of 3004)
3004 / 3 = 1001.3333333333 (the remainder is 1, so 3 is not a divisor of 3004)
...
3004 / 53 = 56.679245283019 (the remainder is 36, so 53 is not a divisor of 3004)
3004 / 54 = 55.62962962963 (the remainder is 34, so 54 is not a divisor of 3004)