What are the divisors of 8016?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 167, 334, 501, 668, 1002, 1336, 2004, 2672, 4008, 8016

There is a total of 20 positive divisors.
The sum of these divisors is 20832.
The arithmetic mean is 1041.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 334, 668, 1002, 1336, 2004, 2672, 4008, 8016

4 odd divisors

1, 3, 167, 501

How to compute the divisors of 8016?

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 8016 by each of the numbers from 1 to 8016 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)

8016 / 1 = 8016 (the remainder is 0, so 1 is a divisor of 8016)
8016 / 2 = 4008 (the remainder is 0, so 2 is a divisor of 8016)
8016 / 3 = 2672 (the remainder is 0, so 3 is a divisor of 8016)
...
8016 / 8015 = 1.0001247660636 (the remainder is 1, so 8015 is not a divisor of 8016)
8016 / 8016 = 1 (the remainder is 0, so 8016 is a divisor of 8016)

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 8016 (i.e. 89.532117142398). 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 $\frac{N}{d} = D$ )

8016 / 1 = 8016 (the remainder is 0, so 1 and 8016 are divisors of 8016)
8016 / 2 = 4008 (the remainder is 0, so 2 and 4008 are divisors of 8016)
8016 / 3 = 2672 (the remainder is 0, so 3 and 2672 are divisors of 8016)
...
8016 / 88 = 91.090909090909 (the remainder is 8, so 88 is not a divisor of 8016)
8016 / 89 = 90.067415730337 (the remainder is 6, so 89 is not a divisor of 8016)