What are the divisors of 2405?

1, 5, 13, 37, 65, 185, 481, 2405

There is a total of 8 positive divisors.
The sum of these divisors is 3192.
The arithmetic mean is 399.

8 odd divisors

1, 5, 13, 37, 65, 185, 481, 2405

How to compute the divisors of 2405?

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 2405 by each of the numbers from 1 to 2405 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)

2405 / 1 = 2405 (the remainder is 0, so 1 is a divisor of 2405)
2405 / 2 = 1202.5 (the remainder is 1, so 2 is not a divisor of 2405)
2405 / 3 = 801.66666666667 (the remainder is 2, so 3 is not a divisor of 2405)
...
2405 / 2404 = 1.0004159733777 (the remainder is 1, so 2404 is not a divisor of 2405)
2405 / 2405 = 1 (the remainder is 0, so 2405 is a divisor of 2405)

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 2405 (i.e. 49.040799340957). 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 $\frac{N}{d} = D$ )

2405 / 1 = 2405 (the remainder is 0, so 1 and 2405 are divisors of 2405)
2405 / 2 = 1202.5 (the remainder is 1, so 2 is not a divisor of 2405)
2405 / 3 = 801.66666666667 (the remainder is 2, so 3 is not a divisor of 2405)
...
2405 / 48 = 50.104166666667 (the remainder is 5, so 48 is not a divisor of 2405)
2405 / 49 = 49.081632653061 (the remainder is 4, so 49 is not a divisor of 2405)