What are the divisors of 9050?

1, 2, 5, 10, 25, 50, 181, 362, 905, 1810, 4525, 9050

There is a total of 12 positive divisors.
The sum of these divisors is 16926.
The arithmetic mean is 1410.5.

6 even divisors

2, 10, 50, 362, 1810, 9050

6 odd divisors

1, 5, 25, 181, 905, 4525

How to compute the divisors of 9050?

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 9050 by each of the numbers from 1 to 9050 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)

9050 / 1 = 9050 (the remainder is 0, so 1 is a divisor of 9050)
9050 / 2 = 4525 (the remainder is 0, so 2 is a divisor of 9050)
9050 / 3 = 3016.6666666667 (the remainder is 2, so 3 is not a divisor of 9050)
...
9050 / 9049 = 1.0001105094486 (the remainder is 1, so 9049 is not a divisor of 9050)
9050 / 9050 = 1 (the remainder is 0, so 9050 is a divisor of 9050)

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 9050 (i.e. 95.131487952202). 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 $\frac{N}{d} = D$ )

9050 / 1 = 9050 (the remainder is 0, so 1 and 9050 are divisors of 9050)
9050 / 2 = 4525 (the remainder is 0, so 2 and 4525 are divisors of 9050)
9050 / 3 = 3016.6666666667 (the remainder is 2, so 3 is not a divisor of 9050)
...
9050 / 94 = 96.276595744681 (the remainder is 26, so 94 is not a divisor of 9050)
9050 / 95 = 95.263157894737 (the remainder is 25, so 95 is not a divisor of 9050)