What are the divisors of 6127?

1, 11, 557, 6127

There is a total of 4 positive divisors.
The sum of these divisors is 6696.
The arithmetic mean is 1674.

4 odd divisors

1, 11, 557, 6127

How to compute the divisors of 6127?

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 6127 by each of the numbers from 1 to 6127 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)

6127 / 1 = 6127 (the remainder is 0, so 1 is a divisor of 6127)
6127 / 2 = 3063.5 (the remainder is 1, so 2 is not a divisor of 6127)
6127 / 3 = 2042.3333333333 (the remainder is 1, so 3 is not a divisor of 6127)
...
6127 / 6126 = 1.0001632386549 (the remainder is 1, so 6126 is not a divisor of 6127)
6127 / 6127 = 1 (the remainder is 0, so 6127 is a divisor of 6127)

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 6127 (i.e. 78.275155700899). 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 $\frac{N}{d} = D$ )

6127 / 1 = 6127 (the remainder is 0, so 1 and 6127 are divisors of 6127)
6127 / 2 = 3063.5 (the remainder is 1, so 2 is not a divisor of 6127)
6127 / 3 = 2042.3333333333 (the remainder is 1, so 3 is not a divisor of 6127)
...
6127 / 77 = 79.571428571429 (the remainder is 44, so 77 is not a divisor of 6127)
6127 / 78 = 78.551282051282 (the remainder is 43, so 78 is not a divisor of 6127)