What are the divisors of 9058?

1, 2, 7, 14, 647, 1294, 4529, 9058

There is a total of 8 positive divisors.
The sum of these divisors is 15552.
The arithmetic mean is 1944.

4 even divisors

2, 14, 1294, 9058

4 odd divisors

1, 7, 647, 4529

How to compute the divisors of 9058?

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 9058 by each of the numbers from 1 to 9058 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)

9058 / 1 = 9058 (the remainder is 0, so 1 is a divisor of 9058)
9058 / 2 = 4529 (the remainder is 0, so 2 is a divisor of 9058)
9058 / 3 = 3019.3333333333 (the remainder is 1, so 3 is not a divisor of 9058)
...
9058 / 9057 = 1.0001104118361 (the remainder is 1, so 9057 is not a divisor of 9058)
9058 / 9058 = 1 (the remainder is 0, so 9058 is a divisor of 9058)

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 9058 (i.e. 95.173525730636). 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 $\frac{N}{d} = D$ )

9058 / 1 = 9058 (the remainder is 0, so 1 and 9058 are divisors of 9058)
9058 / 2 = 4529 (the remainder is 0, so 2 and 4529 are divisors of 9058)
9058 / 3 = 3019.3333333333 (the remainder is 1, so 3 is not a divisor of 9058)
...
9058 / 94 = 96.36170212766 (the remainder is 34, so 94 is not a divisor of 9058)
9058 / 95 = 95.347368421053 (the remainder is 33, so 95 is not a divisor of 9058)