What are the divisors of 9220?

1, 2, 4, 5, 10, 20, 461, 922, 1844, 2305, 4610, 9220

There is a total of 12 positive divisors.
The sum of these divisors is 19404.
The arithmetic mean is 1617.

8 even divisors

2, 4, 10, 20, 922, 1844, 4610, 9220

4 odd divisors

1, 5, 461, 2305

How to compute the divisors of 9220?

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 9220 by each of the numbers from 1 to 9220 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)

9220 / 1 = 9220 (the remainder is 0, so 1 is a divisor of 9220)
9220 / 2 = 4610 (the remainder is 0, so 2 is a divisor of 9220)
9220 / 3 = 3073.3333333333 (the remainder is 1, so 3 is not a divisor of 9220)
...
9220 / 9219 = 1.0001084716347 (the remainder is 1, so 9219 is not a divisor of 9220)
9220 / 9220 = 1 (the remainder is 0, so 9220 is a divisor of 9220)

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 9220 (i.e. 96.020831073262). 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 $\frac{N}{d} = D$ )

9220 / 1 = 9220 (the remainder is 0, so 1 and 9220 are divisors of 9220)
9220 / 2 = 4610 (the remainder is 0, so 2 and 4610 are divisors of 9220)
9220 / 3 = 3073.3333333333 (the remainder is 1, so 3 is not a divisor of 9220)
...
9220 / 95 = 97.052631578947 (the remainder is 5, so 95 is not a divisor of 9220)
9220 / 96 = 96.041666666667 (the remainder is 4, so 96 is not a divisor of 9220)