What are the divisors of 6023?

1, 19, 317, 6023

There is a total of 4 positive divisors.
The sum of these divisors is 6360.
The arithmetic mean is 1590.

4 odd divisors

1, 19, 317, 6023

How to compute the divisors of 6023?

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 6023 by each of the numbers from 1 to 6023 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)

6023 / 1 = 6023 (the remainder is 0, so 1 is a divisor of 6023)
6023 / 2 = 3011.5 (the remainder is 1, so 2 is not a divisor of 6023)
6023 / 3 = 2007.6666666667 (the remainder is 2, so 3 is not a divisor of 6023)
...
6023 / 6022 = 1.0001660577881 (the remainder is 1, so 6022 is not a divisor of 6023)
6023 / 6023 = 1 (the remainder is 0, so 6023 is a divisor of 6023)

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 6023 (i.e. 77.607989279455). 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 $\frac{N}{d} = D$ )

6023 / 1 = 6023 (the remainder is 0, so 1 and 6023 are divisors of 6023)
6023 / 2 = 3011.5 (the remainder is 1, so 2 is not a divisor of 6023)
6023 / 3 = 2007.6666666667 (the remainder is 2, so 3 is not a divisor of 6023)
...
6023 / 76 = 79.25 (the remainder is 19, so 76 is not a divisor of 6023)
6023 / 77 = 78.220779220779 (the remainder is 17, so 77 is not a divisor of 6023)