What are the divisors of 2126?

1, 2, 1063, 2126

There is a total of 4 positive divisors.
The sum of these divisors is 3192.
The arithmetic mean is 798.

2 even divisors

2, 2126

2 odd divisors

1, 1063

How to compute the divisors of 2126?

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 2126 by each of the numbers from 1 to 2126 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)

2126 / 1 = 2126 (the remainder is 0, so 1 is a divisor of 2126)
2126 / 2 = 1063 (the remainder is 0, so 2 is a divisor of 2126)
2126 / 3 = 708.66666666667 (the remainder is 2, so 3 is not a divisor of 2126)
...
2126 / 2125 = 1.0004705882353 (the remainder is 1, so 2125 is not a divisor of 2126)
2126 / 2126 = 1 (the remainder is 0, so 2126 is a divisor of 2126)

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 2126 (i.e. 46.108567533594). 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 $\frac{N}{d} = D$ )

2126 / 1 = 2126 (the remainder is 0, so 1 and 2126 are divisors of 2126)
2126 / 2 = 1063 (the remainder is 0, so 2 and 1063 are divisors of 2126)
2126 / 3 = 708.66666666667 (the remainder is 2, so 3 is not a divisor of 2126)
...
2126 / 45 = 47.244444444444 (the remainder is 11, so 45 is not a divisor of 2126)
2126 / 46 = 46.217391304348 (the remainder is 10, so 46 is not a divisor of 2126)