What are the divisors of 8042?

1, 2, 4021, 8042

There is a total of 4 positive divisors.
The sum of these divisors is 12066.
The arithmetic mean is 3016.5.

2 even divisors

2, 8042

2 odd divisors

1, 4021

How to compute the divisors of 8042?

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 8042 by each of the numbers from 1 to 8042 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)

8042 / 1 = 8042 (the remainder is 0, so 1 is a divisor of 8042)
8042 / 2 = 4021 (the remainder is 0, so 2 is a divisor of 8042)
8042 / 3 = 2680.6666666667 (the remainder is 2, so 3 is not a divisor of 8042)
...
8042 / 8041 = 1.0001243626415 (the remainder is 1, so 8041 is not a divisor of 8042)
8042 / 8042 = 1 (the remainder is 0, so 8042 is a divisor of 8042)

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 8042 (i.e. 89.677198885781). 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 $\frac{N}{d} = D$ )

8042 / 1 = 8042 (the remainder is 0, so 1 and 8042 are divisors of 8042)
8042 / 2 = 4021 (the remainder is 0, so 2 and 4021 are divisors of 8042)
8042 / 3 = 2680.6666666667 (the remainder is 2, so 3 is not a divisor of 8042)
...
8042 / 88 = 91.386363636364 (the remainder is 34, so 88 is not a divisor of 8042)
8042 / 89 = 90.359550561798 (the remainder is 32, so 89 is not a divisor of 8042)