What are the divisors of 9194?

1, 2, 4597, 9194

There is a total of 4 positive divisors.
The sum of these divisors is 13794.
The arithmetic mean is 3448.5.

2 even divisors

2, 9194

2 odd divisors

1, 4597

How to compute the divisors of 9194?

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 9194 by each of the numbers from 1 to 9194 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)

9194 / 1 = 9194 (the remainder is 0, so 1 is a divisor of 9194)
9194 / 2 = 4597 (the remainder is 0, so 2 is a divisor of 9194)
9194 / 3 = 3064.6666666667 (the remainder is 2, so 3 is not a divisor of 9194)
...
9194 / 9193 = 1.0001087784184 (the remainder is 1, so 9193 is not a divisor of 9194)
9194 / 9194 = 1 (the remainder is 0, so 9194 is a divisor of 9194)

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 9194 (i.e. 95.885348202945). 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 $\frac{N}{d} = D$ )

9194 / 1 = 9194 (the remainder is 0, so 1 and 9194 are divisors of 9194)
9194 / 2 = 4597 (the remainder is 0, so 2 and 4597 are divisors of 9194)
9194 / 3 = 3064.6666666667 (the remainder is 2, so 3 is not a divisor of 9194)
...
9194 / 94 = 97.808510638298 (the remainder is 76, so 94 is not a divisor of 9194)
9194 / 95 = 96.778947368421 (the remainder is 74, so 95 is not a divisor of 9194)