What are the divisors of 8019?

1, 3, 9, 11, 27, 33, 81, 99, 243, 297, 729, 891, 2673, 8019

There is a total of 14 positive divisors.
The sum of these divisors is 13116.
The arithmetic mean is 936.85714285714.

14 odd divisors

1, 3, 9, 11, 27, 33, 81, 99, 243, 297, 729, 891, 2673, 8019

How to compute the divisors of 8019?

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 8019 by each of the numbers from 1 to 8019 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)

8019 / 1 = 8019 (the remainder is 0, so 1 is a divisor of 8019)
8019 / 2 = 4009.5 (the remainder is 1, so 2 is not a divisor of 8019)
8019 / 3 = 2673 (the remainder is 0, so 3 is a divisor of 8019)
...
8019 / 8018 = 1.0001247193814 (the remainder is 1, so 8018 is not a divisor of 8019)
8019 / 8019 = 1 (the remainder is 0, so 8019 is a divisor of 8019)

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 8019 (i.e. 89.548869339596). 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 $\frac{N}{d} = D$ )

8019 / 1 = 8019 (the remainder is 0, so 1 and 8019 are divisors of 8019)
8019 / 2 = 4009.5 (the remainder is 1, so 2 is not a divisor of 8019)
8019 / 3 = 2673 (the remainder is 0, so 3 and 2673 are divisors of 8019)
...
8019 / 88 = 91.125 (the remainder is 11, so 88 is not a divisor of 8019)
8019 / 89 = 90.101123595506 (the remainder is 9, so 89 is not a divisor of 8019)