What are the divisors of 2087?

1, 2087

There is a total of 2 positive divisors.
The sum of these divisors is 2088.
The arithmetic mean is 1044.

2 odd divisors

1, 2087

How to compute the divisors of 2087?

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 2087 by each of the numbers from 1 to 2087 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)

2087 / 1 = 2087 (the remainder is 0, so 1 is a divisor of 2087)
2087 / 2 = 1043.5 (the remainder is 1, so 2 is not a divisor of 2087)
2087 / 3 = 695.66666666667 (the remainder is 2, so 3 is not a divisor of 2087)
...
2087 / 2086 = 1.0004793863854 (the remainder is 1, so 2086 is not a divisor of 2087)
2087 / 2087 = 1 (the remainder is 0, so 2087 is a divisor of 2087)

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 2087 (i.e. 45.683695122002). 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 $\frac{N}{d} = D$ )

2087 / 1 = 2087 (the remainder is 0, so 1 and 2087 are divisors of 2087)
2087 / 2 = 1043.5 (the remainder is 1, so 2 is not a divisor of 2087)
2087 / 3 = 695.66666666667 (the remainder is 2, so 3 is not a divisor of 2087)
...
2087 / 44 = 47.431818181818 (the remainder is 19, so 44 is not a divisor of 2087)
2087 / 45 = 46.377777777778 (the remainder is 17, so 45 is not a divisor of 2087)