What are the divisors of 9063?

1, 3, 9, 19, 53, 57, 159, 171, 477, 1007, 3021, 9063

There is a total of 12 positive divisors.
The sum of these divisors is 14040.
The arithmetic mean is 1170.

12 odd divisors

1, 3, 9, 19, 53, 57, 159, 171, 477, 1007, 3021, 9063

How to compute the divisors of 9063?

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 9063 by each of the numbers from 1 to 9063 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)

9063 / 1 = 9063 (the remainder is 0, so 1 is a divisor of 9063)
9063 / 2 = 4531.5 (the remainder is 1, so 2 is not a divisor of 9063)
9063 / 3 = 3021 (the remainder is 0, so 3 is a divisor of 9063)
...
9063 / 9062 = 1.0001103509159 (the remainder is 1, so 9062 is not a divisor of 9063)
9063 / 9063 = 1 (the remainder is 0, so 9063 is a divisor of 9063)

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 9063 (i.e. 95.199789915735). 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 $\frac{N}{d} = D$ )

9063 / 1 = 9063 (the remainder is 0, so 1 and 9063 are divisors of 9063)
9063 / 2 = 4531.5 (the remainder is 1, so 2 is not a divisor of 9063)
9063 / 3 = 3021 (the remainder is 0, so 3 and 3021 are divisors of 9063)
...
9063 / 94 = 96.414893617021 (the remainder is 39, so 94 is not a divisor of 9063)
9063 / 95 = 95.4 (the remainder is 38, so 95 is not a divisor of 9063)