What are the divisors of 6129?

1, 3, 9, 27, 227, 681, 2043, 6129

There is a total of 8 positive divisors.
The sum of these divisors is 9120.
The arithmetic mean is 1140.

8 odd divisors

1, 3, 9, 27, 227, 681, 2043, 6129

How to compute the divisors of 6129?

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 6129 by each of the numbers from 1 to 6129 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)

6129 / 1 = 6129 (the remainder is 0, so 1 is a divisor of 6129)
6129 / 2 = 3064.5 (the remainder is 1, so 2 is not a divisor of 6129)
6129 / 3 = 2043 (the remainder is 0, so 3 is a divisor of 6129)
...
6129 / 6128 = 1.0001631853786 (the remainder is 1, so 6128 is not a divisor of 6129)
6129 / 6129 = 1 (the remainder is 0, so 6129 is a divisor of 6129)

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 6129 (i.e. 78.287930104199). 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 $\frac{N}{d} = D$ )

6129 / 1 = 6129 (the remainder is 0, so 1 and 6129 are divisors of 6129)
6129 / 2 = 3064.5 (the remainder is 1, so 2 is not a divisor of 6129)
6129 / 3 = 2043 (the remainder is 0, so 3 and 2043 are divisors of 6129)
...
6129 / 77 = 79.597402597403 (the remainder is 46, so 77 is not a divisor of 6129)
6129 / 78 = 78.576923076923 (the remainder is 45, so 78 is not a divisor of 6129)