What are the divisors of 8021?

1, 13, 617, 8021

There is a total of 4 positive divisors.
The sum of these divisors is 8652.
The arithmetic mean is 2163.

4 odd divisors

1, 13, 617, 8021

How to compute the divisors of 8021?

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 8021 by each of the numbers from 1 to 8021 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)

8021 / 1 = 8021 (the remainder is 0, so 1 is a divisor of 8021)
8021 / 2 = 4010.5 (the remainder is 1, so 2 is not a divisor of 8021)
8021 / 3 = 2673.6666666667 (the remainder is 2, so 3 is not a divisor of 8021)
...
8021 / 8020 = 1.0001246882793 (the remainder is 1, so 8020 is not a divisor of 8021)
8021 / 8021 = 1 (the remainder is 0, so 8021 is a divisor of 8021)

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 8021 (i.e. 89.56003573023). 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 $\frac{N}{d} = D$ )

8021 / 1 = 8021 (the remainder is 0, so 1 and 8021 are divisors of 8021)
8021 / 2 = 4010.5 (the remainder is 1, so 2 is not a divisor of 8021)
8021 / 3 = 2673.6666666667 (the remainder is 2, so 3 is not a divisor of 8021)
...
8021 / 88 = 91.147727272727 (the remainder is 13, so 88 is not a divisor of 8021)
8021 / 89 = 90.123595505618 (the remainder is 11, so 89 is not a divisor of 8021)