3367 Multiplied by 2-Digit Number

Theorem

In order to multiply $3367$ by a $2$-digit integer $\sqbrk {xy}$:

divide the $6$-digit integer $\sqbrk {xyxyxy}$ by $3$.


Proof

We have that:

$10101 = 3367 \times 3$

Then:

$10101 \times \sqbrk {xy} = \sqbrk {xyxyxy}$

The result follows.

$\blacksquare$


Sources

  • 1975: Martin Gardner: Mathematical Carnival: Chapter $7$: Tricks of Lightning Calculators: Addendum
  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3367$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3367$
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