What are the divisors of 8020?

1, 2, 4, 5, 10, 20, 401, 802, 1604, 2005, 4010, 8020

There is a total of 12 positive divisors.
The sum of these divisors is 16884.
The arithmetic mean is 1407.

8 even divisors

2, 4, 10, 20, 802, 1604, 4010, 8020

4 odd divisors

1, 5, 401, 2005

How to compute the divisors of 8020?

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 8020 by each of the numbers from 1 to 8020 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)

8020 / 1 = 8020 (the remainder is 0, so 1 is a divisor of 8020)
8020 / 2 = 4010 (the remainder is 0, so 2 is a divisor of 8020)
8020 / 3 = 2673.3333333333 (the remainder is 1, so 3 is not a divisor of 8020)
...
8020 / 8019 = 1.0001247038284 (the remainder is 1, so 8019 is not a divisor of 8020)
8020 / 8020 = 1 (the remainder is 0, so 8020 is a divisor of 8020)

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 8020 (i.e. 89.554452708952). 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 $\frac{N}{d} = D$ )

8020 / 1 = 8020 (the remainder is 0, so 1 and 8020 are divisors of 8020)
8020 / 2 = 4010 (the remainder is 0, so 2 and 4010 are divisors of 8020)
8020 / 3 = 2673.3333333333 (the remainder is 1, so 3 is not a divisor of 8020)
...
8020 / 88 = 91.136363636364 (the remainder is 12, so 88 is not a divisor of 8020)
8020 / 89 = 90.112359550562 (the remainder is 10, so 89 is not a divisor of 8020)