What are the divisors of 8056?

1, 2, 4, 8, 19, 38, 53, 76, 106, 152, 212, 424, 1007, 2014, 4028, 8056

There is a total of 16 positive divisors.
The sum of these divisors is 16200.
The arithmetic mean is 1012.5.

12 even divisors

2, 4, 8, 38, 76, 106, 152, 212, 424, 2014, 4028, 8056

4 odd divisors

1, 19, 53, 1007

How to compute the divisors of 8056?

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 8056 by each of the numbers from 1 to 8056 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)

8056 / 1 = 8056 (the remainder is 0, so 1 is a divisor of 8056)
8056 / 2 = 4028 (the remainder is 0, so 2 is a divisor of 8056)
8056 / 3 = 2685.3333333333 (the remainder is 1, so 3 is not a divisor of 8056)
...
8056 / 8055 = 1.0001241464929 (the remainder is 1, so 8055 is not a divisor of 8056)
8056 / 8056 = 1 (the remainder is 0, so 8056 is a divisor of 8056)

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 8056 (i.e. 89.755222689267). 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 $\frac{N}{d} = D$ )

8056 / 1 = 8056 (the remainder is 0, so 1 and 8056 are divisors of 8056)
8056 / 2 = 4028 (the remainder is 0, so 2 and 4028 are divisors of 8056)
8056 / 3 = 2685.3333333333 (the remainder is 1, so 3 is not a divisor of 8056)
...
8056 / 88 = 91.545454545455 (the remainder is 48, so 88 is not a divisor of 8056)
8056 / 89 = 90.516853932584 (the remainder is 46, so 89 is not a divisor of 8056)