Properties of 47,619

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Theorem

If you split $047 \, 619$ into two halves, they add up to $666$:

$047 + 619 = 666$

which is a multiple of $333$.

and:

$047 \, 619 = 143 \times 333$

Similarly, you can split $047 \, 619$ into three thirds, and these add up to $99$:

$04 + 76 + 19 = 99$

and:

$047 \, 619 = 481 \times 99$

The square of $47 \, 619$:

$47 \, 619^2 = 2 \, 267 \, 569 \, 161$

can itself be split into two $6$-digit halves which together add to the recurring part of $\dfrac 4 7$:

$2267 + 569 \, 161 = 571 \, 428$

This is caused by the fact that $047 \, 619$ is the recurring part of the Reciprocal of 21:

$\dfrac 1 {21} = 0 \cdotp \dot 04761 \, \dot 9$

where $21$ is the product of (the smallest) $2$ distinct primes which do not divide $10$.

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $47,619$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $47,619$