What are the divisors of 2721?

1, 3, 907, 2721

There is a total of 4 positive divisors.
The sum of these divisors is 3632.
The arithmetic mean is 908.

4 odd divisors

1, 3, 907, 2721

How to compute the divisors of 2721?

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 2721 by each of the numbers from 1 to 2721 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)

2721 / 1 = 2721 (the remainder is 0, so 1 is a divisor of 2721)
2721 / 2 = 1360.5 (the remainder is 1, so 2 is not a divisor of 2721)
2721 / 3 = 907 (the remainder is 0, so 3 is a divisor of 2721)
...
2721 / 2720 = 1.0003676470588 (the remainder is 1, so 2720 is not a divisor of 2721)
2721 / 2721 = 1 (the remainder is 0, so 2721 is a divisor of 2721)

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 2721 (i.e. 52.16320542298). 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 $\frac{N}{d} = D$ )

2721 / 1 = 2721 (the remainder is 0, so 1 and 2721 are divisors of 2721)
2721 / 2 = 1360.5 (the remainder is 1, so 2 is not a divisor of 2721)
2721 / 3 = 907 (the remainder is 0, so 3 and 907 are divisors of 2721)
...
2721 / 51 = 53.352941176471 (the remainder is 18, so 51 is not a divisor of 2721)
2721 / 52 = 52.326923076923 (the remainder is 17, so 52 is not a divisor of 2721)