Factorial Number System/Examples/2000

Example of Number expressed in Factorial Number System

$2000$ can be expressed in factoradic as:

$2000_{10} = 243 \, 110_!$


\(\ds 2000\) \(=\) \(\ds 2 \times 6! + 560\) as $6! = 720$
\(\ds \) \(=\) \(\ds 2 \times 6! + 4 \times 5! + 80\) as $5! = 120$
\(\ds \) \(=\) \(\ds 2 \times 6! + 4 \times 5! + 3 \times 4! + 8\) as $4! = 24$
\(\ds \) \(=\) \(\ds 2 \times 6! + 4 \times 5! + 3 \times 4! + 1 \times 3! + 2\) as $3! = 6$
\(\ds \) \(=\) \(\ds 2 \times 6! + 4 \times 5! + 3 \times 4! + 1 \times 3! + 1 \times 2!\) as $2! = 2$
\(\ds \) \(=\) \(\ds 2 \times 6! + 4 \times 5! + 3 \times 4! + 1 \times 3! + 1 \times 2! + 0 \times 1!\)


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$