A problem from my book

Number Theory Level pending

Function \(f(n)\) is defined as the sum of digits of \(n\) being repeated until that sum becomes a single digit. For example, [f(123456)=(1+2+3+4+5+6)=(21)=(2+1)=(3)=3.

Find the value of \( F(2612000!) \).

Notation:
\(!\) denotes the factorial notation. For example, \(10! = 1\times2\times3\times\cdots\times10 \).

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