What are the divisors of 9124?

1, 2, 4, 2281, 4562, 9124

There is a total of 6 positive divisors.
The sum of these divisors is 15974.
The arithmetic mean is 2662.3333333333.

4 even divisors

2, 4, 4562, 9124

2 odd divisors

1, 2281

How to compute the divisors of 9124?

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 9124 by each of the numbers from 1 to 9124 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)

9124 / 1 = 9124 (the remainder is 0, so 1 is a divisor of 9124)
9124 / 2 = 4562 (the remainder is 0, so 2 is a divisor of 9124)
9124 / 3 = 3041.3333333333 (the remainder is 1, so 3 is not a divisor of 9124)
...
9124 / 9123 = 1.0001096130659 (the remainder is 1, so 9123 is not a divisor of 9124)
9124 / 9124 = 1 (the remainder is 0, so 9124 is a divisor of 9124)

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 9124 (i.e. 95.519631490076). 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 $\frac{N}{d} = D$ )

9124 / 1 = 9124 (the remainder is 0, so 1 and 9124 are divisors of 9124)
9124 / 2 = 4562 (the remainder is 0, so 2 and 4562 are divisors of 9124)
9124 / 3 = 3041.3333333333 (the remainder is 1, so 3 is not a divisor of 9124)
...
9124 / 94 = 97.063829787234 (the remainder is 6, so 94 is not a divisor of 9124)
9124 / 95 = 96.042105263158 (the remainder is 4, so 95 is not a divisor of 9124)