What are the divisors of 9223?

1, 23, 401, 9223

There is a total of 4 positive divisors.
The sum of these divisors is 9648.
The arithmetic mean is 2412.

4 odd divisors

1, 23, 401, 9223

How to compute the divisors of 9223?

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 9223 by each of the numbers from 1 to 9223 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)

9223 / 1 = 9223 (the remainder is 0, so 1 is a divisor of 9223)
9223 / 2 = 4611.5 (the remainder is 1, so 2 is not a divisor of 9223)
9223 / 3 = 3074.3333333333 (the remainder is 1, so 3 is not a divisor of 9223)
...
9223 / 9222 = 1.0001084363479 (the remainder is 1, so 9222 is not a divisor of 9223)
9223 / 9223 = 1 (the remainder is 0, so 9223 is a divisor of 9223)

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 9223 (i.e. 96.036451412992). 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 $\frac{N}{d} = D$ )

9223 / 1 = 9223 (the remainder is 0, so 1 and 9223 are divisors of 9223)
9223 / 2 = 4611.5 (the remainder is 1, so 2 is not a divisor of 9223)
9223 / 3 = 3074.3333333333 (the remainder is 1, so 3 is not a divisor of 9223)
...
9223 / 95 = 97.084210526316 (the remainder is 8, so 95 is not a divisor of 9223)
9223 / 96 = 96.072916666667 (the remainder is 7, so 96 is not a divisor of 9223)