What are the divisors of 2063?

1, 2063

There is a total of 2 positive divisors.
The sum of these divisors is 2064.
The arithmetic mean is 1032.

2 odd divisors

1, 2063

How to compute the divisors of 2063?

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 2063 by each of the numbers from 1 to 2063 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)

2063 / 1 = 2063 (the remainder is 0, so 1 is a divisor of 2063)
2063 / 2 = 1031.5 (the remainder is 1, so 2 is not a divisor of 2063)
2063 / 3 = 687.66666666667 (the remainder is 2, so 3 is not a divisor of 2063)
...
2063 / 2062 = 1.0004849660524 (the remainder is 1, so 2062 is not a divisor of 2063)
2063 / 2063 = 1 (the remainder is 0, so 2063 is a divisor of 2063)

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 2063 (i.e. 45.420259796703). 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 $\frac{N}{d} = D$ )

2063 / 1 = 2063 (the remainder is 0, so 1 and 2063 are divisors of 2063)
2063 / 2 = 1031.5 (the remainder is 1, so 2 is not a divisor of 2063)
2063 / 3 = 687.66666666667 (the remainder is 2, so 3 is not a divisor of 2063)
...
2063 / 44 = 46.886363636364 (the remainder is 39, so 44 is not a divisor of 2063)
2063 / 45 = 45.844444444444 (the remainder is 38, so 45 is not a divisor of 2063)