What are the divisors of 2786?

1, 2, 7, 14, 199, 398, 1393, 2786

There is a total of 8 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 600.

4 even divisors

2, 14, 398, 2786

4 odd divisors

1, 7, 199, 1393

How to compute the divisors of 2786?

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 2786 by each of the numbers from 1 to 2786 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)

2786 / 1 = 2786 (the remainder is 0, so 1 is a divisor of 2786)
2786 / 2 = 1393 (the remainder is 0, so 2 is a divisor of 2786)
2786 / 3 = 928.66666666667 (the remainder is 2, so 3 is not a divisor of 2786)
...
2786 / 2785 = 1.0003590664273 (the remainder is 1, so 2785 is not a divisor of 2786)
2786 / 2786 = 1 (the remainder is 0, so 2786 is a divisor of 2786)

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 2786 (i.e. 52.782572881587). 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 $\frac{N}{d} = D$ )

2786 / 1 = 2786 (the remainder is 0, so 1 and 2786 are divisors of 2786)
2786 / 2 = 1393 (the remainder is 0, so 2 and 1393 are divisors of 2786)
2786 / 3 = 928.66666666667 (the remainder is 2, so 3 is not a divisor of 2786)
...
2786 / 51 = 54.627450980392 (the remainder is 32, so 51 is not a divisor of 2786)
2786 / 52 = 53.576923076923 (the remainder is 30, so 52 is not a divisor of 2786)