What are the divisors of 9020?

1, 2, 4, 5, 10, 11, 20, 22, 41, 44, 55, 82, 110, 164, 205, 220, 410, 451, 820, 902, 1804, 2255, 4510, 9020

There is a total of 24 positive divisors.
The sum of these divisors is 21168.
The arithmetic mean is 882.

16 even divisors

2, 4, 10, 20, 22, 44, 82, 110, 164, 220, 410, 820, 902, 1804, 4510, 9020

8 odd divisors

1, 5, 11, 41, 55, 205, 451, 2255

How to compute the divisors of 9020?

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 9020 by each of the numbers from 1 to 9020 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)

9020 / 1 = 9020 (the remainder is 0, so 1 is a divisor of 9020)
9020 / 2 = 4510 (the remainder is 0, so 2 is a divisor of 9020)
9020 / 3 = 3006.6666666667 (the remainder is 2, so 3 is not a divisor of 9020)
...
9020 / 9019 = 1.0001108770374 (the remainder is 1, so 9019 is not a divisor of 9020)
9020 / 9020 = 1 (the remainder is 0, so 9020 is a divisor of 9020)

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 9020 (i.e. 94.97368056467). 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 $\frac{N}{d} = D$ )

9020 / 1 = 9020 (the remainder is 0, so 1 and 9020 are divisors of 9020)
9020 / 2 = 4510 (the remainder is 0, so 2 and 4510 are divisors of 9020)
9020 / 3 = 3006.6666666667 (the remainder is 2, so 3 is not a divisor of 9020)
...
9020 / 93 = 96.989247311828 (the remainder is 92, so 93 is not a divisor of 9020)
9020 / 94 = 95.957446808511 (the remainder is 90, so 94 is not a divisor of 9020)