What are the divisors of 9134?

1, 2, 4567, 9134

There is a total of 4 positive divisors.
The sum of these divisors is 13704.
The arithmetic mean is 3426.

2 even divisors

2, 9134

2 odd divisors

1, 4567

How to compute the divisors of 9134?

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 9134 by each of the numbers from 1 to 9134 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)

9134 / 1 = 9134 (the remainder is 0, so 1 is a divisor of 9134)
9134 / 2 = 4567 (the remainder is 0, so 2 is a divisor of 9134)
9134 / 3 = 3044.6666666667 (the remainder is 2, so 3 is not a divisor of 9134)
...
9134 / 9133 = 1.0001094930472 (the remainder is 1, so 9133 is not a divisor of 9134)
9134 / 9134 = 1 (the remainder is 0, so 9134 is a divisor of 9134)

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 9134 (i.e. 95.571962415763). 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 $\frac{N}{d} = D$ )

9134 / 1 = 9134 (the remainder is 0, so 1 and 9134 are divisors of 9134)
9134 / 2 = 4567 (the remainder is 0, so 2 and 4567 are divisors of 9134)
9134 / 3 = 3044.6666666667 (the remainder is 2, so 3 is not a divisor of 9134)
...
9134 / 94 = 97.170212765957 (the remainder is 16, so 94 is not a divisor of 9134)
9134 / 95 = 96.147368421053 (the remainder is 14, so 95 is not a divisor of 9134)