What are the divisors of 6057?

1, 3, 9, 673, 2019, 6057

There is a total of 6 positive divisors.
The sum of these divisors is 8762.
The arithmetic mean is 1460.3333333333.

6 odd divisors

1, 3, 9, 673, 2019, 6057

How to compute the divisors of 6057?

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 6057 by each of the numbers from 1 to 6057 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)

6057 / 1 = 6057 (the remainder is 0, so 1 is a divisor of 6057)
6057 / 2 = 3028.5 (the remainder is 1, so 2 is not a divisor of 6057)
6057 / 3 = 2019 (the remainder is 0, so 3 is a divisor of 6057)
...
6057 / 6056 = 1.0001651254954 (the remainder is 1, so 6056 is not a divisor of 6057)
6057 / 6057 = 1 (the remainder is 0, so 6057 is a divisor of 6057)

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 6057 (i.e. 77.826730626437). 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 $\frac{N}{d} = D$ )

6057 / 1 = 6057 (the remainder is 0, so 1 and 6057 are divisors of 6057)
6057 / 2 = 3028.5 (the remainder is 1, so 2 is not a divisor of 6057)
6057 / 3 = 2019 (the remainder is 0, so 3 and 2019 are divisors of 6057)
...
6057 / 76 = 79.697368421053 (the remainder is 53, so 76 is not a divisor of 6057)
6057 / 77 = 78.662337662338 (the remainder is 51, so 77 is not a divisor of 6057)