What are the divisors of 9148?

1, 2, 4, 2287, 4574, 9148

There is a total of 6 positive divisors.
The sum of these divisors is 16016.
The arithmetic mean is 2669.3333333333.

4 even divisors

2, 4, 4574, 9148

2 odd divisors

1, 2287

How to compute the divisors of 9148?

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 9148 by each of the numbers from 1 to 9148 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)

9148 / 1 = 9148 (the remainder is 0, so 1 is a divisor of 9148)
9148 / 2 = 4574 (the remainder is 0, so 2 is a divisor of 9148)
9148 / 3 = 3049.3333333333 (the remainder is 1, so 3 is not a divisor of 9148)
...
9148 / 9147 = 1.0001093254619 (the remainder is 1, so 9147 is not a divisor of 9148)
9148 / 9148 = 1 (the remainder is 0, so 9148 is a divisor of 9148)

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 9148 (i.e. 95.645177609747). 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 $\frac{N}{d} = D$ )

9148 / 1 = 9148 (the remainder is 0, so 1 and 9148 are divisors of 9148)
9148 / 2 = 4574 (the remainder is 0, so 2 and 4574 are divisors of 9148)
9148 / 3 = 3049.3333333333 (the remainder is 1, so 3 is not a divisor of 9148)
...
9148 / 94 = 97.31914893617 (the remainder is 30, so 94 is not a divisor of 9148)
9148 / 95 = 96.294736842105 (the remainder is 28, so 95 is not a divisor of 9148)