Can We Cancel Out The Factorials?

Number Theory Level 1

( ( n ! ) ! ) ! = ( 24 ! ) ! \large ((n!)!)! =(24!)!

Find the value of n n satisfying the equation above.

5 2 3 4

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Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Rishabh Jain
Mar 18, 2016

Write RHS as ( ( 4 ! ) ! ) ! \large ((4!)!)! and hence

( ( n ! ) ! ) ! = ( ( 4 ! ) ! ) ! \Large ((\color{#D61F06} n!)!)! = ((\color{#D61F06} 4!)!)!

⟹ n = 4 \implies \huge n=\boxed 4

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Right. It is just that simple. Thanks!

Chung Kevin - 5 years, 2 months ago

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Welcome.. .. Well, nice set of factorial problems :-)

Rishabh Jain - 5 years, 2 months ago
Pham Khanh
Apr 19, 2016

( ( n ! ) ! ) ! = ( ( 24 ) ! ) ! ) ((\color{#20A900}{n!})!)!=((\color{#20A900}{24})!)!) ⟹ n ! = 24 \implies \color{#20A900}{n!}=\color{#20A900}{24} ⟹ x = 4 \implies \large \color{#20A900}{\boxed{\color{#20A900}{x=4}}}

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