What are the divisors of 2727?

1, 3, 9, 27, 101, 303, 909, 2727

There is a total of 8 positive divisors.
The sum of these divisors is 4080.
The arithmetic mean is 510.

8 odd divisors

1, 3, 9, 27, 101, 303, 909, 2727

How to compute the divisors of 2727?

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 2727 by each of the numbers from 1 to 2727 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)

2727 / 1 = 2727 (the remainder is 0, so 1 is a divisor of 2727)
2727 / 2 = 1363.5 (the remainder is 1, so 2 is not a divisor of 2727)
2727 / 3 = 909 (the remainder is 0, so 3 is a divisor of 2727)
...
2727 / 2726 = 1.0003668378577 (the remainder is 1, so 2726 is not a divisor of 2727)
2727 / 2727 = 1 (the remainder is 0, so 2727 is a divisor of 2727)

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 2727 (i.e. 52.220685556588). 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 $\frac{N}{d} = D$ )

2727 / 1 = 2727 (the remainder is 0, so 1 and 2727 are divisors of 2727)
2727 / 2 = 1363.5 (the remainder is 1, so 2 is not a divisor of 2727)
2727 / 3 = 909 (the remainder is 0, so 3 and 909 are divisors of 2727)
...
2727 / 51 = 53.470588235294 (the remainder is 24, so 51 is not a divisor of 2727)
2727 / 52 = 52.442307692308 (the remainder is 23, so 52 is not a divisor of 2727)