What are the divisors of 9034?

1, 2, 4517, 9034

There is a total of 4 positive divisors.
The sum of these divisors is 13554.
The arithmetic mean is 3388.5.

2 even divisors

2, 9034

2 odd divisors

1, 4517

How to compute the divisors of 9034?

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 9034 by each of the numbers from 1 to 9034 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)

9034 / 1 = 9034 (the remainder is 0, so 1 is a divisor of 9034)
9034 / 2 = 4517 (the remainder is 0, so 2 is a divisor of 9034)
9034 / 3 = 3011.3333333333 (the remainder is 1, so 3 is not a divisor of 9034)
...
9034 / 9033 = 1.0001107051921 (the remainder is 1, so 9033 is not a divisor of 9034)
9034 / 9034 = 1 (the remainder is 0, so 9034 is a divisor of 9034)

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 9034 (i.e. 95.047356617636). 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 $\frac{N}{d} = D$ )

9034 / 1 = 9034 (the remainder is 0, so 1 and 9034 are divisors of 9034)
9034 / 2 = 4517 (the remainder is 0, so 2 and 4517 are divisors of 9034)
9034 / 3 = 3011.3333333333 (the remainder is 1, so 3 is not a divisor of 9034)
...
9034 / 94 = 96.106382978723 (the remainder is 10, so 94 is not a divisor of 9034)
9034 / 95 = 95.094736842105 (the remainder is 9, so 95 is not a divisor of 9034)