What are the divisors of 6131?

1, 6131

There is a total of 2 positive divisors.
The sum of these divisors is 6132.
The arithmetic mean is 3066.

2 odd divisors

1, 6131

How to compute the divisors of 6131?

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 6131 by each of the numbers from 1 to 6131 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)

6131 / 1 = 6131 (the remainder is 0, so 1 is a divisor of 6131)
6131 / 2 = 3065.5 (the remainder is 1, so 2 is not a divisor of 6131)
6131 / 3 = 2043.6666666667 (the remainder is 2, so 3 is not a divisor of 6131)
...
6131 / 6130 = 1.000163132137 (the remainder is 1, so 6130 is not a divisor of 6131)
6131 / 6131 = 1 (the remainder is 0, so 6131 is a divisor of 6131)

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 6131 (i.e. 78.300702423414). 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 $\frac{N}{d} = D$ )

6131 / 1 = 6131 (the remainder is 0, so 1 and 6131 are divisors of 6131)
6131 / 2 = 3065.5 (the remainder is 1, so 2 is not a divisor of 6131)
6131 / 3 = 2043.6666666667 (the remainder is 2, so 3 is not a divisor of 6131)
...
6131 / 77 = 79.623376623377 (the remainder is 48, so 77 is not a divisor of 6131)
6131 / 78 = 78.602564102564 (the remainder is 47, so 78 is not a divisor of 6131)