What are the divisors of 3005?

1, 5, 601, 3005

There is a total of 4 positive divisors.
The sum of these divisors is 3612.
The arithmetic mean is 903.

4 odd divisors

1, 5, 601, 3005

How to compute the divisors of 3005?

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 3005 by each of the numbers from 1 to 3005 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)

3005 / 1 = 3005 (the remainder is 0, so 1 is a divisor of 3005)
3005 / 2 = 1502.5 (the remainder is 1, so 2 is not a divisor of 3005)
3005 / 3 = 1001.6666666667 (the remainder is 2, so 3 is not a divisor of 3005)
...
3005 / 3004 = 1.0003328894807 (the remainder is 1, so 3004 is not a divisor of 3005)
3005 / 3005 = 1 (the remainder is 0, so 3005 is a divisor of 3005)

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 3005 (i.e. 54.817880294663). 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 $\frac{N}{d} = D$ )

3005 / 1 = 3005 (the remainder is 0, so 1 and 3005 are divisors of 3005)
3005 / 2 = 1502.5 (the remainder is 1, so 2 is not a divisor of 3005)
3005 / 3 = 1001.6666666667 (the remainder is 2, so 3 is not a divisor of 3005)
...
3005 / 53 = 56.698113207547 (the remainder is 37, so 53 is not a divisor of 3005)
3005 / 54 = 55.648148148148 (the remainder is 35, so 54 is not a divisor of 3005)