What are the divisors of 8073?

1, 3, 9, 13, 23, 27, 39, 69, 117, 207, 299, 351, 621, 897, 2691, 8073

There is a total of 16 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 840.

16 odd divisors

1, 3, 9, 13, 23, 27, 39, 69, 117, 207, 299, 351, 621, 897, 2691, 8073

How to compute the divisors of 8073?

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 8073 by each of the numbers from 1 to 8073 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)

8073 / 1 = 8073 (the remainder is 0, so 1 is a divisor of 8073)
8073 / 2 = 4036.5 (the remainder is 1, so 2 is not a divisor of 8073)
8073 / 3 = 2691 (the remainder is 0, so 3 is a divisor of 8073)
...
8073 / 8072 = 1.0001238850347 (the remainder is 1, so 8072 is not a divisor of 8073)
8073 / 8073 = 1 (the remainder is 0, so 8073 is a divisor of 8073)

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 8073 (i.e. 89.849874791232). 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 $\frac{N}{d} = D$ )

8073 / 1 = 8073 (the remainder is 0, so 1 and 8073 are divisors of 8073)
8073 / 2 = 4036.5 (the remainder is 1, so 2 is not a divisor of 8073)
8073 / 3 = 2691 (the remainder is 0, so 3 and 2691 are divisors of 8073)
...
8073 / 88 = 91.738636363636 (the remainder is 65, so 88 is not a divisor of 8073)
8073 / 89 = 90.707865168539 (the remainder is 63, so 89 is not a divisor of 8073)