What are the divisors of 8034?

1, 2, 3, 6, 13, 26, 39, 78, 103, 206, 309, 618, 1339, 2678, 4017, 8034

There is a total of 16 positive divisors.
The sum of these divisors is 17472.
The arithmetic mean is 1092.

8 even divisors

2, 6, 26, 78, 206, 618, 2678, 8034

8 odd divisors

1, 3, 13, 39, 103, 309, 1339, 4017

How to compute the divisors of 8034?

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 8034 by each of the numbers from 1 to 8034 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)

8034 / 1 = 8034 (the remainder is 0, so 1 is a divisor of 8034)
8034 / 2 = 4017 (the remainder is 0, so 2 is a divisor of 8034)
8034 / 3 = 2678 (the remainder is 0, so 3 is a divisor of 8034)
...
8034 / 8033 = 1.0001244864932 (the remainder is 1, so 8033 is not a divisor of 8034)
8034 / 8034 = 1 (the remainder is 0, so 8034 is a divisor of 8034)

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 8034 (i.e. 89.632583361186). 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 $\frac{N}{d} = D$ )

8034 / 1 = 8034 (the remainder is 0, so 1 and 8034 are divisors of 8034)
8034 / 2 = 4017 (the remainder is 0, so 2 and 4017 are divisors of 8034)
8034 / 3 = 2678 (the remainder is 0, so 3 and 2678 are divisors of 8034)
...
8034 / 88 = 91.295454545455 (the remainder is 26, so 88 is not a divisor of 8034)
8034 / 89 = 90.269662921348 (the remainder is 24, so 89 is not a divisor of 8034)