What are the divisors of 7004?

1, 2, 4, 17, 34, 68, 103, 206, 412, 1751, 3502, 7004

There is a total of 12 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 1092.

8 even divisors

2, 4, 34, 68, 206, 412, 3502, 7004

4 odd divisors

1, 17, 103, 1751

How to compute the divisors of 7004?

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 7004 by each of the numbers from 1 to 7004 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)

7004 / 1 = 7004 (the remainder is 0, so 1 is a divisor of 7004)
7004 / 2 = 3502 (the remainder is 0, so 2 is a divisor of 7004)
7004 / 3 = 2334.6666666667 (the remainder is 2, so 3 is not a divisor of 7004)
...
7004 / 7003 = 1.0001427959446 (the remainder is 1, so 7003 is not a divisor of 7004)
7004 / 7004 = 1 (the remainder is 0, so 7004 is a divisor of 7004)

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 7004 (i.e. 83.689903811631). 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 $\frac{N}{d} = D$ )

7004 / 1 = 7004 (the remainder is 0, so 1 and 7004 are divisors of 7004)
7004 / 2 = 3502 (the remainder is 0, so 2 and 3502 are divisors of 7004)
7004 / 3 = 2334.6666666667 (the remainder is 2, so 3 is not a divisor of 7004)
...
7004 / 82 = 85.414634146341 (the remainder is 34, so 82 is not a divisor of 7004)
7004 / 83 = 84.385542168675 (the remainder is 32, so 83 is not a divisor of 7004)