What are the divisors of 9059?

1, 9059

There is a total of 2 positive divisors.
The sum of these divisors is 9060.
The arithmetic mean is 4530.

2 odd divisors

1, 9059

How to compute the divisors of 9059?

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 9059 by each of the numbers from 1 to 9059 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)

9059 / 1 = 9059 (the remainder is 0, so 1 is a divisor of 9059)
9059 / 2 = 4529.5 (the remainder is 1, so 2 is not a divisor of 9059)
9059 / 3 = 3019.6666666667 (the remainder is 2, so 3 is not a divisor of 9059)
...
9059 / 9058 = 1.0001103996467 (the remainder is 1, so 9058 is not a divisor of 9059)
9059 / 9059 = 1 (the remainder is 0, so 9059 is a divisor of 9059)

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 9059 (i.e. 95.178779147455). 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 $\frac{N}{d} = D$ )

9059 / 1 = 9059 (the remainder is 0, so 1 and 9059 are divisors of 9059)
9059 / 2 = 4529.5 (the remainder is 1, so 2 is not a divisor of 9059)
9059 / 3 = 3019.6666666667 (the remainder is 2, so 3 is not a divisor of 9059)
...
9059 / 94 = 96.372340425532 (the remainder is 35, so 94 is not a divisor of 9059)
9059 / 95 = 95.357894736842 (the remainder is 34, so 95 is not a divisor of 9059)