What are the divisors of 6147?

1, 3, 9, 683, 2049, 6147

There is a total of 6 positive divisors.
The sum of these divisors is 8892.
The arithmetic mean is 1482.

6 odd divisors

1, 3, 9, 683, 2049, 6147

How to compute the divisors of 6147?

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 6147 by each of the numbers from 1 to 6147 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)

6147 / 1 = 6147 (the remainder is 0, so 1 is a divisor of 6147)
6147 / 2 = 3073.5 (the remainder is 1, so 2 is not a divisor of 6147)
6147 / 3 = 2049 (the remainder is 0, so 3 is a divisor of 6147)
...
6147 / 6146 = 1.000162707452 (the remainder is 1, so 6146 is not a divisor of 6147)
6147 / 6147 = 1 (the remainder is 0, so 6147 is a divisor of 6147)

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 6147 (i.e. 78.402806072232). 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 $\frac{N}{d} = D$ )

6147 / 1 = 6147 (the remainder is 0, so 1 and 6147 are divisors of 6147)
6147 / 2 = 3073.5 (the remainder is 1, so 2 is not a divisor of 6147)
6147 / 3 = 2049 (the remainder is 0, so 3 and 2049 are divisors of 6147)
...
6147 / 77 = 79.831168831169 (the remainder is 64, so 77 is not a divisor of 6147)
6147 / 78 = 78.807692307692 (the remainder is 63, so 78 is not a divisor of 6147)