What are the divisors of 8024?

1, 2, 4, 8, 17, 34, 59, 68, 118, 136, 236, 472, 1003, 2006, 4012, 8024

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, 34, 68, 118, 136, 236, 472, 2006, 4012, 8024

4 odd divisors

1, 17, 59, 1003

How to compute the divisors of 8024?

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 8024 by each of the numbers from 1 to 8024 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)

8024 / 1 = 8024 (the remainder is 0, so 1 is a divisor of 8024)
8024 / 2 = 4012 (the remainder is 0, so 2 is a divisor of 8024)
8024 / 3 = 2674.6666666667 (the remainder is 2, so 3 is not a divisor of 8024)
...
8024 / 8023 = 1.0001246416552 (the remainder is 1, so 8023 is not a divisor of 8024)
8024 / 8024 = 1 (the remainder is 0, so 8024 is a divisor of 8024)

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 8024 (i.e. 89.576782706235). 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 $\frac{N}{d} = D$ )

8024 / 1 = 8024 (the remainder is 0, so 1 and 8024 are divisors of 8024)
8024 / 2 = 4012 (the remainder is 0, so 2 and 4012 are divisors of 8024)
8024 / 3 = 2674.6666666667 (the remainder is 2, so 3 is not a divisor of 8024)
...
8024 / 88 = 91.181818181818 (the remainder is 16, so 88 is not a divisor of 8024)
8024 / 89 = 90.157303370787 (the remainder is 14, so 89 is not a divisor of 8024)