What are the divisors of 6063?

1, 3, 43, 47, 129, 141, 2021, 6063

There is a total of 8 positive divisors.
The sum of these divisors is 8448.
The arithmetic mean is 1056.

8 odd divisors

1, 3, 43, 47, 129, 141, 2021, 6063

How to compute the divisors of 6063?

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 6063 by each of the numbers from 1 to 6063 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)

6063 / 1 = 6063 (the remainder is 0, so 1 is a divisor of 6063)
6063 / 2 = 3031.5 (the remainder is 1, so 2 is not a divisor of 6063)
6063 / 3 = 2021 (the remainder is 0, so 3 is a divisor of 6063)
...
6063 / 6062 = 1.0001649620587 (the remainder is 1, so 6062 is not a divisor of 6063)
6063 / 6063 = 1 (the remainder is 0, so 6063 is a divisor of 6063)

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 6063 (i.e. 77.865268252283). 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 $\frac{N}{d} = D$ )

6063 / 1 = 6063 (the remainder is 0, so 1 and 6063 are divisors of 6063)
6063 / 2 = 3031.5 (the remainder is 1, so 2 is not a divisor of 6063)
6063 / 3 = 2021 (the remainder is 0, so 3 and 2021 are divisors of 6063)
...
6063 / 76 = 79.776315789474 (the remainder is 59, so 76 is not a divisor of 6063)
6063 / 77 = 78.74025974026 (the remainder is 57, so 77 is not a divisor of 6063)