What are the divisors of 6135?

1, 3, 5, 15, 409, 1227, 2045, 6135

There is a total of 8 positive divisors.
The sum of these divisors is 9840.
The arithmetic mean is 1230.

8 odd divisors

1, 3, 5, 15, 409, 1227, 2045, 6135

How to compute the divisors of 6135?

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 6135 by each of the numbers from 1 to 6135 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)

6135 / 1 = 6135 (the remainder is 0, so 1 is a divisor of 6135)
6135 / 2 = 3067.5 (the remainder is 1, so 2 is not a divisor of 6135)
6135 / 3 = 2045 (the remainder is 0, so 3 is a divisor of 6135)
...
6135 / 6134 = 1.0001630257581 (the remainder is 1, so 6134 is not a divisor of 6135)
6135 / 6135 = 1 (the remainder is 0, so 6135 is a divisor of 6135)

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 6135 (i.e. 78.326240813663). 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 $\frac{N}{d} = D$ )

6135 / 1 = 6135 (the remainder is 0, so 1 and 6135 are divisors of 6135)
6135 / 2 = 3067.5 (the remainder is 1, so 2 is not a divisor of 6135)
6135 / 3 = 2045 (the remainder is 0, so 3 and 2045 are divisors of 6135)
...
6135 / 77 = 79.675324675325 (the remainder is 52, so 77 is not a divisor of 6135)
6135 / 78 = 78.653846153846 (the remainder is 51, so 78 is not a divisor of 6135)