What are the divisors of 2127?

1, 3, 709, 2127

There is a total of 4 positive divisors.
The sum of these divisors is 2840.
The arithmetic mean is 710.

4 odd divisors

1, 3, 709, 2127

How to compute the divisors of 2127?

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 2127 by each of the numbers from 1 to 2127 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)

2127 / 1 = 2127 (the remainder is 0, so 1 is a divisor of 2127)
2127 / 2 = 1063.5 (the remainder is 1, so 2 is not a divisor of 2127)
2127 / 3 = 709 (the remainder is 0, so 3 is a divisor of 2127)
...
2127 / 2126 = 1.0004703668862 (the remainder is 1, so 2126 is not a divisor of 2127)
2127 / 2127 = 1 (the remainder is 0, so 2127 is a divisor of 2127)

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 2127 (i.e. 46.119410230401). 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 $\frac{N}{d} = D$ )

2127 / 1 = 2127 (the remainder is 0, so 1 and 2127 are divisors of 2127)
2127 / 2 = 1063.5 (the remainder is 1, so 2 is not a divisor of 2127)
2127 / 3 = 709 (the remainder is 0, so 3 and 709 are divisors of 2127)
...
2127 / 45 = 47.266666666667 (the remainder is 12, so 45 is not a divisor of 2127)
2127 / 46 = 46.239130434783 (the remainder is 11, so 46 is not a divisor of 2127)