Login
0
June 26, 2020, 7:01 p.m.
If K! has exactly 6 prime factors, how many values of K can exist?

I am weak in number system.

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

Options are

1. 1
2. 2
3. 3
4. 4
quant
cat
numbers
Add Comment to Question
ANSWERS
0
June 29, 2020, 6:07 p.m.

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

1. 2
2. 3
3. 5
4. 7
5. 11
6. 13
7. 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 :)

Add Comment to Answer
In Order to answer this Question please login
Tags
quant
numbers
cat-2019
varc
rc
set-theory
time-speed-distance
quadratic
geometry
cat
Stats
Total Questions
57
Total Answers
32