What are the divisors of 2806?

1, 2, 23, 46, 61, 122, 1403, 2806

There is a total of 8 positive divisors.
The sum of these divisors is 4464.
The arithmetic mean is 558.

4 even divisors

2, 46, 122, 2806

4 odd divisors

1, 23, 61, 1403

How to compute the divisors of 2806?

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 2806 by each of the numbers from 1 to 2806 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)

2806 / 1 = 2806 (the remainder is 0, so 1 is a divisor of 2806)
2806 / 2 = 1403 (the remainder is 0, so 2 is a divisor of 2806)
2806 / 3 = 935.33333333333 (the remainder is 1, so 3 is not a divisor of 2806)
...
2806 / 2805 = 1.0003565062389 (the remainder is 1, so 2805 is not a divisor of 2806)
2806 / 2806 = 1 (the remainder is 0, so 2806 is a divisor of 2806)

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 2806 (i.e. 52.971690552596). 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 $\frac{N}{d} = D$ )

2806 / 1 = 2806 (the remainder is 0, so 1 and 2806 are divisors of 2806)
2806 / 2 = 1403 (the remainder is 0, so 2 and 1403 are divisors of 2806)
2806 / 3 = 935.33333333333 (the remainder is 1, so 3 is not a divisor of 2806)
...
2806 / 51 = 55.019607843137 (the remainder is 1, so 51 is not a divisor of 2806)
2806 / 52 = 53.961538461538 (the remainder is 50, so 52 is not a divisor of 2806)