What are the divisors of 9076?

1, 2, 4, 2269, 4538, 9076

There is a total of 6 positive divisors.
The sum of these divisors is 15890.
The arithmetic mean is 2648.3333333333.

4 even divisors

2, 4, 4538, 9076

2 odd divisors

1, 2269

How to compute the divisors of 9076?

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 9076 by each of the numbers from 1 to 9076 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)

9076 / 1 = 9076 (the remainder is 0, so 1 is a divisor of 9076)
9076 / 2 = 4538 (the remainder is 0, so 2 is a divisor of 9076)
9076 / 3 = 3025.3333333333 (the remainder is 1, so 3 is not a divisor of 9076)
...
9076 / 9075 = 1.0001101928375 (the remainder is 1, so 9075 is not a divisor of 9076)
9076 / 9076 = 1 (the remainder is 0, so 9076 is a divisor of 9076)

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 9076 (i.e. 95.268042910516). 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 $\frac{N}{d} = D$ )

9076 / 1 = 9076 (the remainder is 0, so 1 and 9076 are divisors of 9076)
9076 / 2 = 4538 (the remainder is 0, so 2 and 4538 are divisors of 9076)
9076 / 3 = 3025.3333333333 (the remainder is 1, so 3 is not a divisor of 9076)
...
9076 / 94 = 96.553191489362 (the remainder is 52, so 94 is not a divisor of 9076)
9076 / 95 = 95.536842105263 (the remainder is 51, so 95 is not a divisor of 9076)