I am weak in number system.

If K! has exactly 6 prime factors, how many values of K can exist?

Options are

- 1
- 2
- 3
- 4

All the numbers between 6th prime number and 7th prime number will be considered including 6th prime number.

- 2
- 3
- 5
- 7
- 11
- 13
- 17

13!, 14! ,15!, 16! has exactly 6 prime factors.

How?

2! has olny 1 prime number (i.e. 2)

3! has 2 prime number (i.e. 2 and 3)

4! has 2 prime number (i.e. 2 and 3)

5! has 3 prime number (i.e. 2, 3, and 5)

6! has 3 prime number (i.e. 2, 3, and 5)

7! has 4 prime number (i.e. 2, 3, 5 and 7)

We see a pattern that every prime number increase unique prime factor by 1.

So, in your case you need number with exactly 6 prime factor.

Therefore, 6th prime number is the number where you can find 6 prime numbers and 7th prime number is where you find 7 prime factor

Therefore, all the numbers form 6th prime number till 7th is your answer :)