What are the divisors of 8134?

1, 2, 7, 14, 49, 83, 98, 166, 581, 1162, 4067, 8134

There is a total of 12 positive divisors.
The sum of these divisors is 14364.
The arithmetic mean is 1197.

6 even divisors

2, 14, 98, 166, 1162, 8134

6 odd divisors

1, 7, 49, 83, 581, 4067

How to compute the divisors of 8134?

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 8134 by each of the numbers from 1 to 8134 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)

8134 / 1 = 8134 (the remainder is 0, so 1 is a divisor of 8134)
8134 / 2 = 4067 (the remainder is 0, so 2 is a divisor of 8134)
8134 / 3 = 2711.3333333333 (the remainder is 1, so 3 is not a divisor of 8134)
...
8134 / 8133 = 1.0001229558588 (the remainder is 1, so 8133 is not a divisor of 8134)
8134 / 8134 = 1 (the remainder is 0, so 8134 is a divisor of 8134)

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 8134 (i.e. 90.188691087076). 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 $\frac{N}{d} = D$ )

8134 / 1 = 8134 (the remainder is 0, so 1 and 8134 are divisors of 8134)
8134 / 2 = 4067 (the remainder is 0, so 2 and 4067 are divisors of 8134)
8134 / 3 = 2711.3333333333 (the remainder is 1, so 3 is not a divisor of 8134)
...
8134 / 89 = 91.393258426966 (the remainder is 35, so 89 is not a divisor of 8134)
8134 / 90 = 90.377777777778 (the remainder is 34, so 90 is not a divisor of 8134)