What are the divisors of 2666?

1, 2, 31, 43, 62, 86, 1333, 2666

There is a total of 8 positive divisors.
The sum of these divisors is 4224.
The arithmetic mean is 528.

4 even divisors

2, 62, 86, 2666

4 odd divisors

1, 31, 43, 1333

How to compute the divisors of 2666?

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 2666 by each of the numbers from 1 to 2666 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)

2666 / 1 = 2666 (the remainder is 0, so 1 is a divisor of 2666)
2666 / 2 = 1333 (the remainder is 0, so 2 is a divisor of 2666)
2666 / 3 = 888.66666666667 (the remainder is 2, so 3 is not a divisor of 2666)
...
2666 / 2665 = 1.0003752345216 (the remainder is 1, so 2665 is not a divisor of 2666)
2666 / 2666 = 1 (the remainder is 0, so 2666 is a divisor of 2666)

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 2666 (i.e. 51.633322573702). 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 $\frac{N}{d} = D$ )

2666 / 1 = 2666 (the remainder is 0, so 1 and 2666 are divisors of 2666)
2666 / 2 = 1333 (the remainder is 0, so 2 and 1333 are divisors of 2666)
2666 / 3 = 888.66666666667 (the remainder is 2, so 3 is not a divisor of 2666)
...
2666 / 50 = 53.32 (the remainder is 16, so 50 is not a divisor of 2666)
2666 / 51 = 52.274509803922 (the remainder is 14, so 51 is not a divisor of 2666)