What are the divisors of 9094?

1, 2, 4547, 9094

There is a total of 4 positive divisors.
The sum of these divisors is 13644.
The arithmetic mean is 3411.

2 even divisors

2, 9094

2 odd divisors

1, 4547

How to compute the divisors of 9094?

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 9094 by each of the numbers from 1 to 9094 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)

9094 / 1 = 9094 (the remainder is 0, so 1 is a divisor of 9094)
9094 / 2 = 4547 (the remainder is 0, so 2 is a divisor of 9094)
9094 / 3 = 3031.3333333333 (the remainder is 1, so 3 is not a divisor of 9094)
...
9094 / 9093 = 1.0001099747058 (the remainder is 1, so 9093 is not a divisor of 9094)
9094 / 9094 = 1 (the remainder is 0, so 9094 is a divisor of 9094)

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 9094 (i.e. 95.362466411057). 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 $\frac{N}{d} = D$ )

9094 / 1 = 9094 (the remainder is 0, so 1 and 9094 are divisors of 9094)
9094 / 2 = 4547 (the remainder is 0, so 2 and 4547 are divisors of 9094)
9094 / 3 = 3031.3333333333 (the remainder is 1, so 3 is not a divisor of 9094)
...
9094 / 94 = 96.744680851064 (the remainder is 70, so 94 is not a divisor of 9094)
9094 / 95 = 95.726315789474 (the remainder is 69, so 95 is not a divisor of 9094)