What are the divisors of 6165?

1, 3, 5, 9, 15, 45, 137, 411, 685, 1233, 2055, 6165

There is a total of 12 positive divisors.
The sum of these divisors is 10764.
The arithmetic mean is 897.

12 odd divisors

1, 3, 5, 9, 15, 45, 137, 411, 685, 1233, 2055, 6165

How to compute the divisors of 6165?

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 6165 by each of the numbers from 1 to 6165 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)

6165 / 1 = 6165 (the remainder is 0, so 1 is a divisor of 6165)
6165 / 2 = 3082.5 (the remainder is 1, so 2 is not a divisor of 6165)
6165 / 3 = 2055 (the remainder is 0, so 3 is a divisor of 6165)
...
6165 / 6164 = 1.0001622323167 (the remainder is 1, so 6164 is not a divisor of 6165)
6165 / 6165 = 1 (the remainder is 0, so 6165 is a divisor of 6165)

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 6165 (i.e. 78.517513969814). 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 $\frac{N}{d} = D$ )

6165 / 1 = 6165 (the remainder is 0, so 1 and 6165 are divisors of 6165)
6165 / 2 = 3082.5 (the remainder is 1, so 2 is not a divisor of 6165)
6165 / 3 = 2055 (the remainder is 0, so 3 and 2055 are divisors of 6165)
...
6165 / 77 = 80.064935064935 (the remainder is 5, so 77 is not a divisor of 6165)
6165 / 78 = 79.038461538462 (the remainder is 3, so 78 is not a divisor of 6165)