What are the divisors of 2605?

1, 5, 521, 2605

There is a total of 4 positive divisors.
The sum of these divisors is 3132.
The arithmetic mean is 783.

4 odd divisors

1, 5, 521, 2605

How to compute the divisors of 2605?

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 2605 by each of the numbers from 1 to 2605 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)

2605 / 1 = 2605 (the remainder is 0, so 1 is a divisor of 2605)
2605 / 2 = 1302.5 (the remainder is 1, so 2 is not a divisor of 2605)
2605 / 3 = 868.33333333333 (the remainder is 1, so 3 is not a divisor of 2605)
...
2605 / 2604 = 1.0003840245776 (the remainder is 1, so 2604 is not a divisor of 2605)
2605 / 2605 = 1 (the remainder is 0, so 2605 is a divisor of 2605)

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 2605 (i.e. 51.039200620699). 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 $\frac{N}{d} = D$ )

2605 / 1 = 2605 (the remainder is 0, so 1 and 2605 are divisors of 2605)
2605 / 2 = 1302.5 (the remainder is 1, so 2 is not a divisor of 2605)
2605 / 3 = 868.33333333333 (the remainder is 1, so 3 is not a divisor of 2605)
...
2605 / 50 = 52.1 (the remainder is 5, so 50 is not a divisor of 2605)
2605 / 51 = 51.078431372549 (the remainder is 4, so 51 is not a divisor of 2605)