What are the divisors of 9182?

1, 2, 4591, 9182

There is a total of 4 positive divisors.
The sum of these divisors is 13776.
The arithmetic mean is 3444.

2 even divisors

2, 9182

2 odd divisors

1, 4591

How to compute the divisors of 9182?

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 9182 by each of the numbers from 1 to 9182 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)

9182 / 1 = 9182 (the remainder is 0, so 1 is a divisor of 9182)
9182 / 2 = 4591 (the remainder is 0, so 2 is a divisor of 9182)
9182 / 3 = 3060.6666666667 (the remainder is 2, so 3 is not a divisor of 9182)
...
9182 / 9181 = 1.0001089205969 (the remainder is 1, so 9181 is not a divisor of 9182)
9182 / 9182 = 1 (the remainder is 0, so 9182 is a divisor of 9182)

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 9182 (i.e. 95.82275303914). 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 $\frac{N}{d} = D$ )

9182 / 1 = 9182 (the remainder is 0, so 1 and 9182 are divisors of 9182)
9182 / 2 = 4591 (the remainder is 0, so 2 and 4591 are divisors of 9182)
9182 / 3 = 3060.6666666667 (the remainder is 2, so 3 is not a divisor of 9182)
...
9182 / 94 = 97.68085106383 (the remainder is 64, so 94 is not a divisor of 9182)
9182 / 95 = 96.652631578947 (the remainder is 62, so 95 is not a divisor of 9182)