What are the divisors of 8136?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 113, 226, 339, 452, 678, 904, 1017, 1356, 2034, 2712, 4068, 8136

There is a total of 24 positive divisors.
The sum of these divisors is 22230.
The arithmetic mean is 926.25.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 226, 452, 678, 904, 1356, 2034, 2712, 4068, 8136

6 odd divisors

1, 3, 9, 113, 339, 1017

How to compute the divisors of 8136?

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 8136 by each of the numbers from 1 to 8136 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)

8136 / 1 = 8136 (the remainder is 0, so 1 is a divisor of 8136)
8136 / 2 = 4068 (the remainder is 0, so 2 is a divisor of 8136)
8136 / 3 = 2712 (the remainder is 0, so 3 is a divisor of 8136)
...
8136 / 8135 = 1.00012292563 (the remainder is 1, so 8135 is not a divisor of 8136)
8136 / 8136 = 1 (the remainder is 0, so 8136 is a divisor of 8136)

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 8136 (i.e. 90.199778270237). 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 $\frac{N}{d} = D$ )

8136 / 1 = 8136 (the remainder is 0, so 1 and 8136 are divisors of 8136)
8136 / 2 = 4068 (the remainder is 0, so 2 and 4068 are divisors of 8136)
8136 / 3 = 2712 (the remainder is 0, so 3 and 2712 are divisors of 8136)
...
8136 / 89 = 91.415730337079 (the remainder is 37, so 89 is not a divisor of 8136)
8136 / 90 = 90.4 (the remainder is 36, so 90 is not a divisor of 8136)