Solution
If 9! is divisible by p^3, where p is a positive integer, how many values of p are possible?
a.2 b.3 c.4 d.5 e.6
Hi Santhosh,
Going forward, while posting a question, kindly let us know your specific doubt.
Like, what you didn’t understand in the question ?, what was your approach ? etc.
That way we could help you better.
Now coming back to this question, 9! is a not a big value, so we can write it (expand it) and figure out the answer.
9! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9
Start substituting, p = 1, 2, 3, 4, 6 definitely divides 9!.
There are seven 2’s, four 3’s , three 4’s and four 6’s are possible in a factorial.
So the answer has to be D(5).
Hope this helps.