What are the divisors of 6083?

1, 7, 11, 77, 79, 553, 869, 6083

There is a total of 8 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 960.

8 odd divisors

1, 7, 11, 77, 79, 553, 869, 6083

How to compute the divisors of 6083?

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 6083 by each of the numbers from 1 to 6083 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)

6083 / 1 = 6083 (the remainder is 0, so 1 is a divisor of 6083)
6083 / 2 = 3041.5 (the remainder is 1, so 2 is not a divisor of 6083)
6083 / 3 = 2027.6666666667 (the remainder is 2, so 3 is not a divisor of 6083)
...
6083 / 6082 = 1.0001644195988 (the remainder is 1, so 6082 is not a divisor of 6083)
6083 / 6083 = 1 (the remainder is 0, so 6083 is a divisor of 6083)

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 6083 (i.e. 77.993589480162). 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 $\frac{N}{d} = D$ )

6083 / 1 = 6083 (the remainder is 0, so 1 and 6083 are divisors of 6083)
6083 / 2 = 3041.5 (the remainder is 1, so 2 is not a divisor of 6083)
6083 / 3 = 2027.6666666667 (the remainder is 2, so 3 is not a divisor of 6083)
...
6083 / 76 = 80.039473684211 (the remainder is 3, so 76 is not a divisor of 6083)
6083 / 77 = 79 (the remainder is 0, so 77 and 79 are divisors of 6083)