What are the divisors of 2687?

1, 2687

There is a total of 2 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 1344.

2 odd divisors

1, 2687

How to compute the divisors of 2687?

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 2687 by each of the numbers from 1 to 2687 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)

2687 / 1 = 2687 (the remainder is 0, so 1 is a divisor of 2687)
2687 / 2 = 1343.5 (the remainder is 1, so 2 is not a divisor of 2687)
2687 / 3 = 895.66666666667 (the remainder is 2, so 3 is not a divisor of 2687)
...
2687 / 2686 = 1.0003723008191 (the remainder is 1, so 2686 is not a divisor of 2687)
2687 / 2687 = 1 (the remainder is 0, so 2687 is a divisor of 2687)

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 2687 (i.e. 51.836280730778). 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 $\frac{N}{d} = D$ )

2687 / 1 = 2687 (the remainder is 0, so 1 and 2687 are divisors of 2687)
2687 / 2 = 1343.5 (the remainder is 1, so 2 is not a divisor of 2687)
2687 / 3 = 895.66666666667 (the remainder is 2, so 3 is not a divisor of 2687)
...
2687 / 50 = 53.74 (the remainder is 37, so 50 is not a divisor of 2687)
2687 / 51 = 52.686274509804 (the remainder is 35, so 51 is not a divisor of 2687)