Factorials

Number Theory Level pending

If x! = (7!)!/7!, what is the value of x ?


The answer is 5039.

Adithya Rajeev by Adithya Rajeev , 23, India

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2 solutions

x ! = ( 7 ! ) ! 7 ! x!=\frac{(7!)!}{7!} ⇒ x ! × 7 ! = ( 7 ! ) ! \Rightarrow x!\times 7!=(7!)! x ! × 5040 = 5040 ! x! \times 5040=5040! x ! = 5040 ! 5040 = 5039 ! ⇒ x = 5039 x!=\frac{5040!}{5040}=5039! \Rightarrow x=\boxed{5039}

I still don't know how not to evaluate 7!

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This problem is equal to my problem Stop shouting!

Drop TheProblem - 5 years, 9 months ago

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That's all right.

Adam Phúc Nguyễn - 5 years, 9 months ago
Adithya Rajeev
Sep 2, 2015

x! = (7!)!/7! .

7! = 5040 .

Therefore,

5040*x! = (5040)! .

=> x! = 5039! .

Therefore x = 5039 .

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