What are the divisors of 9046?

1, 2, 4523, 9046

There is a total of 4 positive divisors.
The sum of these divisors is 13572.
The arithmetic mean is 3393.

2 even divisors

2, 9046

2 odd divisors

1, 4523

How to compute the divisors of 9046?

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 9046 by each of the numbers from 1 to 9046 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)

9046 / 1 = 9046 (the remainder is 0, so 1 is a divisor of 9046)
9046 / 2 = 4523 (the remainder is 0, so 2 is a divisor of 9046)
9046 / 3 = 3015.3333333333 (the remainder is 1, so 3 is not a divisor of 9046)
...
9046 / 9045 = 1.0001105583195 (the remainder is 1, so 9045 is not a divisor of 9046)
9046 / 9046 = 1 (the remainder is 0, so 9046 is a divisor of 9046)

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 9046 (i.e. 95.110462095397). 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 $\frac{N}{d} = D$ )

9046 / 1 = 9046 (the remainder is 0, so 1 and 9046 are divisors of 9046)
9046 / 2 = 4523 (the remainder is 0, so 2 and 4523 are divisors of 9046)
9046 / 3 = 3015.3333333333 (the remainder is 1, so 3 is not a divisor of 9046)
...
9046 / 94 = 96.234042553191 (the remainder is 22, so 94 is not a divisor of 9046)
9046 / 95 = 95.221052631579 (the remainder is 21, so 95 is not a divisor of 9046)