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

Intermediate Asked on September 28, 2017 in Problem Solving.
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1 Answer(s)

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.

 

Expert Answered on September 29, 2017.
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