What are the divisors of 9210?

1, 2, 3, 5, 6, 10, 15, 30, 307, 614, 921, 1535, 1842, 3070, 4605, 9210

There is a total of 16 positive divisors.
The sum of these divisors is 22176.
The arithmetic mean is 1386.

8 even divisors

2, 6, 10, 30, 614, 1842, 3070, 9210

8 odd divisors

1, 3, 5, 15, 307, 921, 1535, 4605

How to compute the divisors of 9210?

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 9210 by each of the numbers from 1 to 9210 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)

9210 / 1 = 9210 (the remainder is 0, so 1 is a divisor of 9210)
9210 / 2 = 4605 (the remainder is 0, so 2 is a divisor of 9210)
9210 / 3 = 3070 (the remainder is 0, so 3 is a divisor of 9210)
...
9210 / 9209 = 1.0001085894234 (the remainder is 1, so 9209 is not a divisor of 9210)
9210 / 9210 = 1 (the remainder is 0, so 9210 is a divisor of 9210)

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 9210 (i.e. 95.968744912081). 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 $\frac{N}{d} = D$ )

9210 / 1 = 9210 (the remainder is 0, so 1 and 9210 are divisors of 9210)
9210 / 2 = 4605 (the remainder is 0, so 2 and 4605 are divisors of 9210)
9210 / 3 = 3070 (the remainder is 0, so 3 and 3070 are divisors of 9210)
...
9210 / 94 = 97.978723404255 (the remainder is 92, so 94 is not a divisor of 9210)
9210 / 95 = 96.947368421053 (the remainder is 90, so 95 is not a divisor of 9210)