What are the divisors of 9043?

1, 9043

There is a total of 2 positive divisors.
The sum of these divisors is 9044.
The arithmetic mean is 4522.

2 odd divisors

1, 9043

How to compute the divisors of 9043?

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 9043 by each of the numbers from 1 to 9043 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)

9043 / 1 = 9043 (the remainder is 0, so 1 is a divisor of 9043)
9043 / 2 = 4521.5 (the remainder is 1, so 2 is not a divisor of 9043)
9043 / 3 = 3014.3333333333 (the remainder is 1, so 3 is not a divisor of 9043)
...
9043 / 9042 = 1.0001105950011 (the remainder is 1, so 9042 is not a divisor of 9043)
9043 / 9043 = 1 (the remainder is 0, so 9043 is a divisor of 9043)

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 9043 (i.e. 95.094689651946). 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 $\frac{N}{d} = D$ )

9043 / 1 = 9043 (the remainder is 0, so 1 and 9043 are divisors of 9043)
9043 / 2 = 4521.5 (the remainder is 1, so 2 is not a divisor of 9043)
9043 / 3 = 3014.3333333333 (the remainder is 1, so 3 is not a divisor of 9043)
...
9043 / 94 = 96.202127659574 (the remainder is 19, so 94 is not a divisor of 9043)
9043 / 95 = 95.189473684211 (the remainder is 18, so 95 is not a divisor of 9043)