What are the divisors of 9057?

1, 3, 3019, 9057

There is a total of 4 positive divisors.
The sum of these divisors is 12080.
The arithmetic mean is 3020.

4 odd divisors

1, 3, 3019, 9057

How to compute the divisors of 9057?

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 9057 by each of the numbers from 1 to 9057 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)

9057 / 1 = 9057 (the remainder is 0, so 1 is a divisor of 9057)
9057 / 2 = 4528.5 (the remainder is 1, so 2 is not a divisor of 9057)
9057 / 3 = 3019 (the remainder is 0, so 3 is a divisor of 9057)
...
9057 / 9056 = 1.0001104240283 (the remainder is 1, so 9056 is not a divisor of 9057)
9057 / 9057 = 1 (the remainder is 0, so 9057 is a divisor of 9057)

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 9057 (i.e. 95.168272023821). 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 $\frac{N}{d} = D$ )

9057 / 1 = 9057 (the remainder is 0, so 1 and 9057 are divisors of 9057)
9057 / 2 = 4528.5 (the remainder is 1, so 2 is not a divisor of 9057)
9057 / 3 = 3019 (the remainder is 0, so 3 and 3019 are divisors of 9057)
...
9057 / 94 = 96.351063829787 (the remainder is 33, so 94 is not a divisor of 9057)
9057 / 95 = 95.336842105263 (the remainder is 32, so 95 is not a divisor of 9057)