What are the divisors of 6183?

1, 3, 9, 27, 229, 687, 2061, 6183

There is a total of 8 positive divisors.
The sum of these divisors is 9200.
The arithmetic mean is 1150.

8 odd divisors

1, 3, 9, 27, 229, 687, 2061, 6183

How to compute the divisors of 6183?

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 6183 by each of the numbers from 1 to 6183 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)

6183 / 1 = 6183 (the remainder is 0, so 1 is a divisor of 6183)
6183 / 2 = 3091.5 (the remainder is 1, so 2 is not a divisor of 6183)
6183 / 3 = 2061 (the remainder is 0, so 3 is a divisor of 6183)
...
6183 / 6182 = 1.0001617599482 (the remainder is 1, so 6182 is not a divisor of 6183)
6183 / 6183 = 1 (the remainder is 0, so 6183 is a divisor of 6183)

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 6183 (i.e. 78.632054532487). 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 $\frac{N}{d} = D$ )

6183 / 1 = 6183 (the remainder is 0, so 1 and 6183 are divisors of 6183)
6183 / 2 = 3091.5 (the remainder is 1, so 2 is not a divisor of 6183)
6183 / 3 = 2061 (the remainder is 0, so 3 and 2061 are divisors of 6183)
...
6183 / 77 = 80.298701298701 (the remainder is 23, so 77 is not a divisor of 6183)
6183 / 78 = 79.269230769231 (the remainder is 21, so 78 is not a divisor of 6183)