What are the divisors of 9178?

1, 2, 13, 26, 353, 706, 4589, 9178

There is a total of 8 positive divisors.
The sum of these divisors is 14868.
The arithmetic mean is 1858.5.

4 even divisors

2, 26, 706, 9178

4 odd divisors

1, 13, 353, 4589

How to compute the divisors of 9178?

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 9178 by each of the numbers from 1 to 9178 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)

9178 / 1 = 9178 (the remainder is 0, so 1 is a divisor of 9178)
9178 / 2 = 4589 (the remainder is 0, so 2 is a divisor of 9178)
9178 / 3 = 3059.3333333333 (the remainder is 1, so 3 is not a divisor of 9178)
...
9178 / 9177 = 1.0001089680724 (the remainder is 1, so 9177 is not a divisor of 9178)
9178 / 9178 = 1 (the remainder is 0, so 9178 is a divisor of 9178)

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 9178 (i.e. 95.80187889598). 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 $\frac{N}{d} = D$ )

9178 / 1 = 9178 (the remainder is 0, so 1 and 9178 are divisors of 9178)
9178 / 2 = 4589 (the remainder is 0, so 2 and 4589 are divisors of 9178)
9178 / 3 = 3059.3333333333 (the remainder is 1, so 3 is not a divisor of 9178)
...
9178 / 94 = 97.63829787234 (the remainder is 60, so 94 is not a divisor of 9178)
9178 / 95 = 96.610526315789 (the remainder is 58, so 95 is not a divisor of 9178)