What are the divisors of 2511?

1, 3, 9, 27, 31, 81, 93, 279, 837, 2511

There is a total of 10 positive divisors.
The sum of these divisors is 3872.
The arithmetic mean is 387.2.

10 odd divisors

1, 3, 9, 27, 31, 81, 93, 279, 837, 2511

How to compute the divisors of 2511?

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 2511 by each of the numbers from 1 to 2511 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)

2511 / 1 = 2511 (the remainder is 0, so 1 is a divisor of 2511)
2511 / 2 = 1255.5 (the remainder is 1, so 2 is not a divisor of 2511)
2511 / 3 = 837 (the remainder is 0, so 3 is a divisor of 2511)
...
2511 / 2510 = 1.0003984063745 (the remainder is 1, so 2510 is not a divisor of 2511)
2511 / 2511 = 1 (the remainder is 0, so 2511 is a divisor of 2511)

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 2511 (i.e. 50.10987926547). 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 $\frac{N}{d} = D$ )

2511 / 1 = 2511 (the remainder is 0, so 1 and 2511 are divisors of 2511)
2511 / 2 = 1255.5 (the remainder is 1, so 2 is not a divisor of 2511)
2511 / 3 = 837 (the remainder is 0, so 3 and 837 are divisors of 2511)
...
2511 / 49 = 51.244897959184 (the remainder is 12, so 49 is not a divisor of 2511)
2511 / 50 = 50.22 (the remainder is 11, so 50 is not a divisor of 2511)