What are the divisors of 8002?

1, 2, 4001, 8002

There is a total of 4 positive divisors.
The sum of these divisors is 12006.
The arithmetic mean is 3001.5.

2 even divisors

2, 8002

2 odd divisors

1, 4001

How to compute the divisors of 8002?

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 8002 by each of the numbers from 1 to 8002 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)

8002 / 1 = 8002 (the remainder is 0, so 1 is a divisor of 8002)
8002 / 2 = 4001 (the remainder is 0, so 2 is a divisor of 8002)
8002 / 3 = 2667.3333333333 (the remainder is 1, so 3 is not a divisor of 8002)
...
8002 / 8001 = 1.000124984377 (the remainder is 1, so 8001 is not a divisor of 8002)
8002 / 8002 = 1 (the remainder is 0, so 8002 is a divisor of 8002)

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 8002 (i.e. 89.453898741195). 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 $\frac{N}{d} = D$ )

8002 / 1 = 8002 (the remainder is 0, so 1 and 8002 are divisors of 8002)
8002 / 2 = 4001 (the remainder is 0, so 2 and 4001 are divisors of 8002)
8002 / 3 = 2667.3333333333 (the remainder is 1, so 3 is not a divisor of 8002)
...
8002 / 88 = 90.931818181818 (the remainder is 82, so 88 is not a divisor of 8002)
8002 / 89 = 89.910112359551 (the remainder is 81, so 89 is not a divisor of 8002)