What are the divisors of 2766?

1, 2, 3, 6, 461, 922, 1383, 2766

There is a total of 8 positive divisors.
The sum of these divisors is 5544.
The arithmetic mean is 693.

4 even divisors

2, 6, 922, 2766

4 odd divisors

1, 3, 461, 1383

How to compute the divisors of 2766?

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 2766 by each of the numbers from 1 to 2766 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)

2766 / 1 = 2766 (the remainder is 0, so 1 is a divisor of 2766)
2766 / 2 = 1383 (the remainder is 0, so 2 is a divisor of 2766)
2766 / 3 = 922 (the remainder is 0, so 3 is a divisor of 2766)
...
2766 / 2765 = 1.0003616636528 (the remainder is 1, so 2765 is not a divisor of 2766)
2766 / 2766 = 1 (the remainder is 0, so 2766 is a divisor of 2766)

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 2766 (i.e. 52.592775169219). 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 $\frac{N}{d} = D$ )

2766 / 1 = 2766 (the remainder is 0, so 1 and 2766 are divisors of 2766)
2766 / 2 = 1383 (the remainder is 0, so 2 and 1383 are divisors of 2766)
2766 / 3 = 922 (the remainder is 0, so 3 and 922 are divisors of 2766)
...
2766 / 51 = 54.235294117647 (the remainder is 12, so 51 is not a divisor of 2766)
2766 / 52 = 53.192307692308 (the remainder is 10, so 52 is not a divisor of 2766)