find the number.

by hemangsarkar, Sep 10, 2012, 6:25 PM

in this question, the representation of the number is not to be confused with the product.



Q) a $6$ digit number ${abcdef}$ when multiplied by $6$ gives ${defabc}$.

find the number.

my solution :

let ${abc}$ be $m$ and ${def}$ be $n$.

then we have $6(10^{3}m + n) = 10^{3}n + m$

or, $5999m =  994n$

or, $857m = 142n$

$m$ and $n$ are three digit numbers.
note that $857$ is a prime number, which is easy to show. i will skip that part.

so we must have $n = 857$ and $m = 142$.

the number is $142857$
This post has been edited 1 time. Last edited by hemangsarkar, Sep 11, 2012, 7:32 AM

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