What are the divisors of 8036?

1, 2, 4, 7, 14, 28, 41, 49, 82, 98, 164, 196, 287, 574, 1148, 2009, 4018, 8036

There is a total of 18 positive divisors.
The sum of these divisors is 16758.
The arithmetic mean is 931.

12 even divisors

2, 4, 14, 28, 82, 98, 164, 196, 574, 1148, 4018, 8036

6 odd divisors

1, 7, 41, 49, 287, 2009

How to compute the divisors of 8036?

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 8036 by each of the numbers from 1 to 8036 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)

8036 / 1 = 8036 (the remainder is 0, so 1 is a divisor of 8036)
8036 / 2 = 4018 (the remainder is 0, so 2 is a divisor of 8036)
8036 / 3 = 2678.6666666667 (the remainder is 2, so 3 is not a divisor of 8036)
...
8036 / 8035 = 1.0001244555072 (the remainder is 1, so 8035 is not a divisor of 8036)
8036 / 8036 = 1 (the remainder is 0, so 8036 is a divisor of 8036)

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 8036 (i.e. 89.64373932406). 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 $\frac{N}{d} = D$ )

8036 / 1 = 8036 (the remainder is 0, so 1 and 8036 are divisors of 8036)
8036 / 2 = 4018 (the remainder is 0, so 2 and 4018 are divisors of 8036)
8036 / 3 = 2678.6666666667 (the remainder is 2, so 3 is not a divisor of 8036)
...
8036 / 88 = 91.318181818182 (the remainder is 28, so 88 is not a divisor of 8036)
8036 / 89 = 90.292134831461 (the remainder is 26, so 89 is not a divisor of 8036)