What are the divisors of 9027?

1, 3, 9, 17, 51, 59, 153, 177, 531, 1003, 3009, 9027

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, 17, 51, 59, 153, 177, 531, 1003, 3009, 9027

How to compute the divisors of 9027?

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 9027 by each of the numbers from 1 to 9027 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)

9027 / 1 = 9027 (the remainder is 0, so 1 is a divisor of 9027)
9027 / 2 = 4513.5 (the remainder is 1, so 2 is not a divisor of 9027)
9027 / 3 = 3009 (the remainder is 0, so 3 is a divisor of 9027)
...
9027 / 9026 = 1.0001107910481 (the remainder is 1, so 9026 is not a divisor of 9027)
9027 / 9027 = 1 (the remainder is 0, so 9027 is a divisor of 9027)

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 9027 (i.e. 95.010525732679). 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 $\frac{N}{d} = D$ )

9027 / 1 = 9027 (the remainder is 0, so 1 and 9027 are divisors of 9027)
9027 / 2 = 4513.5 (the remainder is 1, so 2 is not a divisor of 9027)
9027 / 3 = 3009 (the remainder is 0, so 3 and 3009 are divisors of 9027)
...
9027 / 94 = 96.031914893617 (the remainder is 3, so 94 is not a divisor of 9027)
9027 / 95 = 95.021052631579 (the remainder is 2, so 95 is not a divisor of 9027)