What are the divisors of 9143?

1, 41, 223, 9143

There is a total of 4 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 2352.

4 odd divisors

1, 41, 223, 9143

How to compute the divisors of 9143?

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 9143 by each of the numbers from 1 to 9143 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)

9143 / 1 = 9143 (the remainder is 0, so 1 is a divisor of 9143)
9143 / 2 = 4571.5 (the remainder is 1, so 2 is not a divisor of 9143)
9143 / 3 = 3047.6666666667 (the remainder is 2, so 3 is not a divisor of 9143)
...
9143 / 9142 = 1.0001093852549 (the remainder is 1, so 9142 is not a divisor of 9143)
9143 / 9143 = 1 (the remainder is 0, so 9143 is a divisor of 9143)

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 9143 (i.e. 95.619035761714). 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 $\frac{N}{d} = D$ )

9143 / 1 = 9143 (the remainder is 0, so 1 and 9143 are divisors of 9143)
9143 / 2 = 4571.5 (the remainder is 1, so 2 is not a divisor of 9143)
9143 / 3 = 3047.6666666667 (the remainder is 2, so 3 is not a divisor of 9143)
...
9143 / 94 = 97.265957446809 (the remainder is 25, so 94 is not a divisor of 9143)
9143 / 95 = 96.242105263158 (the remainder is 23, so 95 is not a divisor of 9143)