What are the divisors of 7005?

1, 3, 5, 15, 467, 1401, 2335, 7005

There is a total of 8 positive divisors.
The sum of these divisors is 11232.
The arithmetic mean is 1404.

8 odd divisors

1, 3, 5, 15, 467, 1401, 2335, 7005

How to compute the divisors of 7005?

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 7005 by each of the numbers from 1 to 7005 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)

7005 / 1 = 7005 (the remainder is 0, so 1 is a divisor of 7005)
7005 / 2 = 3502.5 (the remainder is 1, so 2 is not a divisor of 7005)
7005 / 3 = 2335 (the remainder is 0, so 3 is a divisor of 7005)
...
7005 / 7004 = 1.0001427755568 (the remainder is 1, so 7004 is not a divisor of 7005)
7005 / 7005 = 1 (the remainder is 0, so 7005 is a divisor of 7005)

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 7005 (i.e. 83.695878034704). 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 $\frac{N}{d} = D$ )

7005 / 1 = 7005 (the remainder is 0, so 1 and 7005 are divisors of 7005)
7005 / 2 = 3502.5 (the remainder is 1, so 2 is not a divisor of 7005)
7005 / 3 = 2335 (the remainder is 0, so 3 and 2335 are divisors of 7005)
...
7005 / 82 = 85.426829268293 (the remainder is 35, so 82 is not a divisor of 7005)
7005 / 83 = 84.397590361446 (the remainder is 33, so 83 is not a divisor of 7005)