6 digit number

a a a a a a = b c × b c ( 2 c b ) ( 2 b + c ) ( c b ) \large\overline{aaaaaa}=\overline{bc} \times b c (2c-b) (2b+c) ( c-b)

If natural numbers a , b , c a,b,c satisfy the above equation , find the product a b c abc .

Details And Assumptions:

  • b c \overline{bc} is a two digit number and a a a a a a \overline{aaaaaa} is a six digit number.

The answer is 84.

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1 solution

Azzim Habibie
Dec 21, 2015

we can write the LHS as 111111a, 111111a = 3×7×11×13×37×a then we put b = 3 and c = 7. Finally we got a = 4. So, abc = 4.3.7 = 84

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