What are the divisors of 9206?

1, 2, 4603, 9206

There is a total of 4 positive divisors.
The sum of these divisors is 13812.
The arithmetic mean is 3453.

2 even divisors

2, 9206

2 odd divisors

1, 4603

How to compute the divisors of 9206?

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 9206 by each of the numbers from 1 to 9206 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)

9206 / 1 = 9206 (the remainder is 0, so 1 is a divisor of 9206)
9206 / 2 = 4603 (the remainder is 0, so 2 is a divisor of 9206)
9206 / 3 = 3068.6666666667 (the remainder is 2, so 3 is not a divisor of 9206)
...
9206 / 9205 = 1.0001086366105 (the remainder is 1, so 9205 is not a divisor of 9206)
9206 / 9206 = 1 (the remainder is 0, so 9206 is a divisor of 9206)

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 9206 (i.e. 95.947902530488). 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 $\frac{N}{d} = D$ )

9206 / 1 = 9206 (the remainder is 0, so 1 and 9206 are divisors of 9206)
9206 / 2 = 4603 (the remainder is 0, so 2 and 4603 are divisors of 9206)
9206 / 3 = 3068.6666666667 (the remainder is 2, so 3 is not a divisor of 9206)
...
9206 / 94 = 97.936170212766 (the remainder is 88, so 94 is not a divisor of 9206)
9206 / 95 = 96.905263157895 (the remainder is 86, so 95 is not a divisor of 9206)