142857 (Number)

The number 142,857 has some interesting mathematical properties. If you multiply the number by 2, 3, 4, 5 or 6 the answer will be an anagram of itself.
olspan=2|142857
a href="/encyclopedia/Cardinal-number" title="Cardinal number">Cardinal One hundred forty-two thousand,
eight hundred and fifty-seven
a href="/encyclopedia/Ordinal-number" title="Ordinal number">Ordinal 142857th
a href="/encyclopedia/Factorization" title="Factorization">Factorization 142857 = 3^3 \cdot 11 \cdot 13 \cdot 37
a href="/encyclopedia/Binary-numeral-system" title="Binary numeral system">Binary 100010111000001001
a href="/encyclopedia/Hexadecimal" title="Hexadecimal">Hexadecimal 22E09
  1 x 142,857 = 142,857  2 x 142,857 = 285,714  3 x 142,857 = 428,571  4 x 142,857 = 571,428  5 x 142,857 = 714,285  6 x 142,857 = 857,142  7 x 142,857 = 999,999 
If you continue multiplying it by larger numbers, the result will always be some sort of variation on 142857 or 999999. For example:
        8 x 142,857 = 1,142,856 (Add the first digit and the last and you get 142857.)       42 x 142,857 = 5,999,994  142,857 x 142,857 = 20,408,122,449 (Add the first five digits to the last six and you get 142857.) 
If you divide it by 2 or by 5 you also get an anagram of itself with decimal point:
  142,857 / 2 = 71,428.5  142,857 / 5 = 28,571.4 
It is also similar to the first few digits of Pi. In base 10, 142,857 is a Harshad number and a Kaprekar number. It is derived from the fraction 1/7 = 0 . 142857 142857 14... 199e05 142857

 

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