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 $

$=$

$\ds 2 \times 6! + 4 \times 5! + 3 \times 4! + 1 \times 3! + 1 \times 2! + 0 \times 1!$