What are the divisors of 6126?

1, 2, 3, 6, 1021, 2042, 3063, 6126

There is a total of 8 positive divisors.
The sum of these divisors is 12264.
The arithmetic mean is 1533.

4 even divisors

2, 6, 2042, 6126

4 odd divisors

1, 3, 1021, 3063

How to compute the divisors of 6126?

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 6126 by each of the numbers from 1 to 6126 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)

6126 / 1 = 6126 (the remainder is 0, so 1 is a divisor of 6126)
6126 / 2 = 3063 (the remainder is 0, so 2 is a divisor of 6126)
6126 / 3 = 2042 (the remainder is 0, so 3 is a divisor of 6126)
...
6126 / 6125 = 1.0001632653061 (the remainder is 1, so 6125 is not a divisor of 6126)
6126 / 6126 = 1 (the remainder is 0, so 6126 is a divisor of 6126)

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 6126 (i.e. 78.268767717398). 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 $\frac{N}{d} = D$ )

6126 / 1 = 6126 (the remainder is 0, so 1 and 6126 are divisors of 6126)
6126 / 2 = 3063 (the remainder is 0, so 2 and 3063 are divisors of 6126)
6126 / 3 = 2042 (the remainder is 0, so 3 and 2042 are divisors of 6126)
...
6126 / 77 = 79.558441558442 (the remainder is 43, so 77 is not a divisor of 6126)
6126 / 78 = 78.538461538462 (the remainder is 42, so 78 is not a divisor of 6126)