Factorial Problem

Number Theory Level 2

Find x x : ( 7 ! ) ! 7 ! = x ! {\dfrac{(7!)!}{7!}=x!}


The answer is 5039.

Mohammed Rizqallah by Mohammed Rizqallah , 23, Jordan

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2 solutions

Chan Tin Ping
Nov 24, 2017

( 7 ! ) ! 7 ! = 1 × 2 × 3 … × ( 7 ! − 2 ) × ( 7 ! − 1 ) × 7 ! 7 ! = 1 × 2 × 3 … × ( 7 ! − 2 ) × ( 7 ! − 1 ) = ( 7 ! − 1 ) ! = 5039 ! \begin{aligned} &\frac{(7!)!}{7!} \\ =&\frac{1\times 2 \times 3 … \times (7!-2) \times (7!-1) \times 7!}{7!} \\ =&1\times 2 \times 3 … \times (7!-2) \times (7!-1) \\ =&(7!-1)! \\ =&5039! \end{aligned}

Hence, n n = 5039 \large 5039

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@Chan Tin Ping Good job

Mohammed Rizqallah - 3 years, 6 months ago

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Thanks (;ω;)(;ω;)

Chan Tin Ping - 3 years, 6 months ago

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but you got 5039! , it's not x ^_* take care of this type of problems

Mohammed Rizqallah - 3 years, 6 months ago

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@Mohammed Rizqallah – Already change, thanks again

Chan Tin Ping - 3 years, 6 months ago

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