What are the divisors of 2730?

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365, 2730

There is a total of 32 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 252.

16 even divisors

2, 6, 10, 14, 26, 30, 42, 70, 78, 130, 182, 210, 390, 546, 910, 2730

16 odd divisors

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365

How to compute the divisors of 2730?

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 2730 by each of the numbers from 1 to 2730 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)

2730 / 1 = 2730 (the remainder is 0, so 1 is a divisor of 2730)
2730 / 2 = 1365 (the remainder is 0, so 2 is a divisor of 2730)
2730 / 3 = 910 (the remainder is 0, so 3 is a divisor of 2730)
...
2730 / 2729 = 1.0003664345914 (the remainder is 1, so 2729 is not a divisor of 2730)
2730 / 2730 = 1 (the remainder is 0, so 2730 is a divisor of 2730)

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 2730 (i.e. 52.249401910453). 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 $\frac{N}{d} = D$ )

2730 / 1 = 2730 (the remainder is 0, so 1 and 2730 are divisors of 2730)
2730 / 2 = 1365 (the remainder is 0, so 2 and 1365 are divisors of 2730)
2730 / 3 = 910 (the remainder is 0, so 3 and 910 are divisors of 2730)
...
2730 / 51 = 53.529411764706 (the remainder is 27, so 51 is not a divisor of 2730)
2730 / 52 = 52.5 (the remainder is 26, so 52 is not a divisor of 2730)