What are the divisors of 2706?

1, 2, 3, 6, 11, 22, 33, 41, 66, 82, 123, 246, 451, 902, 1353, 2706

There is a total of 16 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 378.

8 even divisors

2, 6, 22, 66, 82, 246, 902, 2706

8 odd divisors

1, 3, 11, 33, 41, 123, 451, 1353

How to compute the divisors of 2706?

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 2706 by each of the numbers from 1 to 2706 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)

2706 / 1 = 2706 (the remainder is 0, so 1 is a divisor of 2706)
2706 / 2 = 1353 (the remainder is 0, so 2 is a divisor of 2706)
2706 / 3 = 902 (the remainder is 0, so 3 is a divisor of 2706)
...
2706 / 2705 = 1.0003696857671 (the remainder is 1, so 2705 is not a divisor of 2706)
2706 / 2706 = 1 (the remainder is 0, so 2706 is a divisor of 2706)

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 2706 (i.e. 52.01922721456). 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 $\frac{N}{d} = D$ )

2706 / 1 = 2706 (the remainder is 0, so 1 and 2706 are divisors of 2706)
2706 / 2 = 1353 (the remainder is 0, so 2 and 1353 are divisors of 2706)
2706 / 3 = 902 (the remainder is 0, so 3 and 902 are divisors of 2706)
...
2706 / 51 = 53.058823529412 (the remainder is 3, so 51 is not a divisor of 2706)
2706 / 52 = 52.038461538462 (the remainder is 2, so 52 is not a divisor of 2706)