What are the divisors of 6019?

1, 13, 463, 6019

There is a total of 4 positive divisors.
The sum of these divisors is 6496.
The arithmetic mean is 1624.

4 odd divisors

1, 13, 463, 6019

How to compute the divisors of 6019?

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 6019 by each of the numbers from 1 to 6019 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)

6019 / 1 = 6019 (the remainder is 0, so 1 is a divisor of 6019)
6019 / 2 = 3009.5 (the remainder is 1, so 2 is not a divisor of 6019)
6019 / 3 = 2006.3333333333 (the remainder is 1, so 3 is not a divisor of 6019)
...
6019 / 6018 = 1.0001661681622 (the remainder is 1, so 6018 is not a divisor of 6019)
6019 / 6019 = 1 (the remainder is 0, so 6019 is a divisor of 6019)

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 6019 (i.e. 77.582214456665). 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 $\frac{N}{d} = D$ )

6019 / 1 = 6019 (the remainder is 0, so 1 and 6019 are divisors of 6019)
6019 / 2 = 3009.5 (the remainder is 1, so 2 is not a divisor of 6019)
6019 / 3 = 2006.3333333333 (the remainder is 1, so 3 is not a divisor of 6019)
...
6019 / 76 = 79.197368421053 (the remainder is 15, so 76 is not a divisor of 6019)
6019 / 77 = 78.168831168831 (the remainder is 13, so 77 is not a divisor of 6019)