What are the divisors of 9023?

1, 7, 1289, 9023

There is a total of 4 positive divisors.
The sum of these divisors is 10320.
The arithmetic mean is 2580.

4 odd divisors

1, 7, 1289, 9023

How to compute the divisors of 9023?

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 9023 by each of the numbers from 1 to 9023 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)

9023 / 1 = 9023 (the remainder is 0, so 1 is a divisor of 9023)
9023 / 2 = 4511.5 (the remainder is 1, so 2 is not a divisor of 9023)
9023 / 3 = 3007.6666666667 (the remainder is 2, so 3 is not a divisor of 9023)
...
9023 / 9022 = 1.0001108401685 (the remainder is 1, so 9022 is not a divisor of 9023)
9023 / 9023 = 1 (the remainder is 0, so 9023 is a divisor of 9023)

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 9023 (i.e. 94.989473100971). 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 $\frac{N}{d} = D$ )

9023 / 1 = 9023 (the remainder is 0, so 1 and 9023 are divisors of 9023)
9023 / 2 = 4511.5 (the remainder is 1, so 2 is not a divisor of 9023)
9023 / 3 = 3007.6666666667 (the remainder is 2, so 3 is not a divisor of 9023)
...
9023 / 93 = 97.021505376344 (the remainder is 2, so 93 is not a divisor of 9023)
9023 / 94 = 95.989361702128 (the remainder is 93, so 94 is not a divisor of 9023)