What are the divisors of 9078?

1, 2, 3, 6, 17, 34, 51, 89, 102, 178, 267, 534, 1513, 3026, 4539, 9078

There is a total of 16 positive divisors.
The sum of these divisors is 19440.
The arithmetic mean is 1215.

8 even divisors

2, 6, 34, 102, 178, 534, 3026, 9078

8 odd divisors

1, 3, 17, 51, 89, 267, 1513, 4539

How to compute the divisors of 9078?

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 9078 by each of the numbers from 1 to 9078 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)

9078 / 1 = 9078 (the remainder is 0, so 1 is a divisor of 9078)
9078 / 2 = 4539 (the remainder is 0, so 2 is a divisor of 9078)
9078 / 3 = 3026 (the remainder is 0, so 3 is a divisor of 9078)
...
9078 / 9077 = 1.0001101685579 (the remainder is 1, so 9077 is not a divisor of 9078)
9078 / 9078 = 1 (the remainder is 0, so 9078 is a divisor of 9078)

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 9078 (i.e. 95.27853903162). 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 $\frac{N}{d} = D$ )

9078 / 1 = 9078 (the remainder is 0, so 1 and 9078 are divisors of 9078)
9078 / 2 = 4539 (the remainder is 0, so 2 and 4539 are divisors of 9078)
9078 / 3 = 3026 (the remainder is 0, so 3 and 3026 are divisors of 9078)
...
9078 / 94 = 96.574468085106 (the remainder is 54, so 94 is not a divisor of 9078)
9078 / 95 = 95.557894736842 (the remainder is 53, so 95 is not a divisor of 9078)