What are the divisors of 2866?

1, 2, 1433, 2866

There is a total of 4 positive divisors.
The sum of these divisors is 4302.
The arithmetic mean is 1075.5.

2 even divisors

2, 2866

2 odd divisors

1, 1433

How to compute the divisors of 2866?

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 2866 by each of the numbers from 1 to 2866 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)

2866 / 1 = 2866 (the remainder is 0, so 1 is a divisor of 2866)
2866 / 2 = 1433 (the remainder is 0, so 2 is a divisor of 2866)
2866 / 3 = 955.33333333333 (the remainder is 1, so 3 is not a divisor of 2866)
...
2866 / 2865 = 1.0003490401396 (the remainder is 1, so 2865 is not a divisor of 2866)
2866 / 2866 = 1 (the remainder is 0, so 2866 is a divisor of 2866)

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 2866 (i.e. 53.535035257297). 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 $\frac{N}{d} = D$ )

2866 / 1 = 2866 (the remainder is 0, so 1 and 2866 are divisors of 2866)
2866 / 2 = 1433 (the remainder is 0, so 2 and 1433 are divisors of 2866)
2866 / 3 = 955.33333333333 (the remainder is 1, so 3 is not a divisor of 2866)
...
2866 / 52 = 55.115384615385 (the remainder is 6, so 52 is not a divisor of 2866)
2866 / 53 = 54.075471698113 (the remainder is 4, so 53 is not a divisor of 2866)