What are the divisors of 2535?

1, 3, 5, 13, 15, 39, 65, 169, 195, 507, 845, 2535

There is a total of 12 positive divisors.
The sum of these divisors is 4392.
The arithmetic mean is 366.

12 odd divisors

1, 3, 5, 13, 15, 39, 65, 169, 195, 507, 845, 2535

How to compute the divisors of 2535?

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 2535 by each of the numbers from 1 to 2535 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)

2535 / 1 = 2535 (the remainder is 0, so 1 is a divisor of 2535)
2535 / 2 = 1267.5 (the remainder is 1, so 2 is not a divisor of 2535)
2535 / 3 = 845 (the remainder is 0, so 3 is a divisor of 2535)
...
2535 / 2534 = 1.0003946329913 (the remainder is 1, so 2534 is not a divisor of 2535)
2535 / 2535 = 1 (the remainder is 0, so 2535 is a divisor of 2535)

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 2535 (i.e. 50.348783500696). 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 $\frac{N}{d} = D$ )

2535 / 1 = 2535 (the remainder is 0, so 1 and 2535 are divisors of 2535)
2535 / 2 = 1267.5 (the remainder is 1, so 2 is not a divisor of 2535)
2535 / 3 = 845 (the remainder is 0, so 3 and 845 are divisors of 2535)
...
2535 / 49 = 51.734693877551 (the remainder is 36, so 49 is not a divisor of 2535)
2535 / 50 = 50.7 (the remainder is 35, so 50 is not a divisor of 2535)