What are the divisors of 2585?

1, 5, 11, 47, 55, 235, 517, 2585

There is a total of 8 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 432.

8 odd divisors

1, 5, 11, 47, 55, 235, 517, 2585

How to compute the divisors of 2585?

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 2585 by each of the numbers from 1 to 2585 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)

2585 / 1 = 2585 (the remainder is 0, so 1 is a divisor of 2585)
2585 / 2 = 1292.5 (the remainder is 1, so 2 is not a divisor of 2585)
2585 / 3 = 861.66666666667 (the remainder is 2, so 3 is not a divisor of 2585)
...
2585 / 2584 = 1.000386996904 (the remainder is 1, so 2584 is not a divisor of 2585)
2585 / 2585 = 1 (the remainder is 0, so 2585 is a divisor of 2585)

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 2585 (i.e. 50.842895275545). 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 $\frac{N}{d} = D$ )

2585 / 1 = 2585 (the remainder is 0, so 1 and 2585 are divisors of 2585)
2585 / 2 = 1292.5 (the remainder is 1, so 2 is not a divisor of 2585)
2585 / 3 = 861.66666666667 (the remainder is 2, so 3 is not a divisor of 2585)
...
2585 / 49 = 52.755102040816 (the remainder is 37, so 49 is not a divisor of 2585)
2585 / 50 = 51.7 (the remainder is 35, so 50 is not a divisor of 2585)