What are the divisors of 9010?

1, 2, 5, 10, 17, 34, 53, 85, 106, 170, 265, 530, 901, 1802, 4505, 9010

There is a total of 16 positive divisors.
The sum of these divisors is 17496.
The arithmetic mean is 1093.5.

8 even divisors

2, 10, 34, 106, 170, 530, 1802, 9010

8 odd divisors

1, 5, 17, 53, 85, 265, 901, 4505

How to compute the divisors of 9010?

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 9010 by each of the numbers from 1 to 9010 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)

9010 / 1 = 9010 (the remainder is 0, so 1 is a divisor of 9010)
9010 / 2 = 4505 (the remainder is 0, so 2 is a divisor of 9010)
9010 / 3 = 3003.3333333333 (the remainder is 1, so 3 is not a divisor of 9010)
...
9010 / 9009 = 1.000111000111 (the remainder is 1, so 9009 is not a divisor of 9010)
9010 / 9010 = 1 (the remainder is 0, so 9010 is a divisor of 9010)

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 9010 (i.e. 94.921019800674). 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 $\frac{N}{d} = D$ )

9010 / 1 = 9010 (the remainder is 0, so 1 and 9010 are divisors of 9010)
9010 / 2 = 4505 (the remainder is 0, so 2 and 4505 are divisors of 9010)
9010 / 3 = 3003.3333333333 (the remainder is 1, so 3 is not a divisor of 9010)
...
9010 / 93 = 96.881720430108 (the remainder is 82, so 93 is not a divisor of 9010)
9010 / 94 = 95.851063829787 (the remainder is 80, so 94 is not a divisor of 9010)