Which of the following is not a factor of 3630 ?

The correct option is 9.

To determine which of the given options is not a factor of 3630, we can use divisibility rules or perform prime factorization on 3630.

Let's check the prime factorization of 3630 step-by-step:

$3630=10\times 363$

$3630=2\times 5\times 3\times 121$

$3630=2\times 3\times 5\times {11}^2$

Now, let's test each option against 3630:

1. 11: Since 11 is present in the prime factorization (${11}^2$), 11 is a factor of 3630.
Indeed, $3630÷11=330$.

2. 3: Since 3 is present in the prime factorization, 3 is a factor of 3630.
Alternatively, the sum of the digits of 3630 is $3+6+3+0=12$, which is divisible by 3.

3. 5: The last digit of 3630 is 0, which means 3630 is divisible by 5. Therefore, 5 is a factor of 3630.

4. 9: For a number to be divisible by 9, the sum of its digits must be a multiple of 9.
The sum of the digits of 3630 is $3+6+3+0=12$.
Since 12 is not divisible by 9, 9 is not a factor of 3630.
Furthermore, looking at the prime factorization, 9 requires $3^2$, but 3630 only has one factor of 3.

Hence, 9 is not a factor of 3630.