What are the divisors of 9198?

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 73, 126, 146, 219, 438, 511, 657, 1022, 1314, 1533, 3066, 4599, 9198

There is a total of 24 positive divisors.
The sum of these divisors is 23088.
The arithmetic mean is 962.

12 even divisors

2, 6, 14, 18, 42, 126, 146, 438, 1022, 1314, 3066, 9198

12 odd divisors

1, 3, 7, 9, 21, 63, 73, 219, 511, 657, 1533, 4599

How to compute the divisors of 9198?

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 9198 by each of the numbers from 1 to 9198 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)

9198 / 1 = 9198 (the remainder is 0, so 1 is a divisor of 9198)
9198 / 2 = 4599 (the remainder is 0, so 2 is a divisor of 9198)
9198 / 3 = 3066 (the remainder is 0, so 3 is a divisor of 9198)
...
9198 / 9197 = 1.000108731108 (the remainder is 1, so 9197 is not a divisor of 9198)
9198 / 9198 = 1 (the remainder is 0, so 9198 is a divisor of 9198)

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 9198 (i.e. 95.906204178875). 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 $\frac{N}{d} = D$ )

9198 / 1 = 9198 (the remainder is 0, so 1 and 9198 are divisors of 9198)
9198 / 2 = 4599 (the remainder is 0, so 2 and 4599 are divisors of 9198)
9198 / 3 = 3066 (the remainder is 0, so 3 and 3066 are divisors of 9198)
...
9198 / 94 = 97.851063829787 (the remainder is 80, so 94 is not a divisor of 9198)
9198 / 95 = 96.821052631579 (the remainder is 78, so 95 is not a divisor of 9198)