Pandigital Properties of 123,456,789

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Theorem

$123 \, 456 \, 789$ has the following properties:

It is pandigital, and remains so when multiplied by $2$, $4$, $5$, $7$ and $8$:

\(\displaystyle 123 \, 456 \, 789 \times 1\) \(=\) \(\displaystyle 123 \, 456 \, 789\)
\(\displaystyle 123 \, 456 \, 789 \times 2\) \(=\) \(\displaystyle 246 \, 913 \, 578\)
\(\displaystyle 123 \, 456 \, 789 \times 3\) \(=\) \(\displaystyle 370 \, 370 \, 367\)
\(\displaystyle 123 \, 456 \, 789 \times 4\) \(=\) \(\displaystyle 493 \, 827 \, 156\)
\(\displaystyle 123 \, 456 \, 789 \times 5\) \(=\) \(\displaystyle 617 \, 283 \, 945\)
\(\displaystyle 123 \, 456 \, 789 \times 6\) \(=\) \(\displaystyle 740 \, 740 \, 734\)
\(\displaystyle 123 \, 456 \, 789 \times 7\) \(=\) \(\displaystyle 864 \, 197 \, 523\)
\(\displaystyle 123 \, 456 \, 789 \times 8\) \(=\) \(\displaystyle 987 \, 654 \, 312\)
\(\displaystyle 123 \, 456 \, 789 \times 9\) \(=\) \(\displaystyle 1 \, 111 \, 111 \, 101\)



Also see


Sources