when a certain number is multiplied by 14 the product obtained is entirely sixes. find the smallest such number.

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Please find below the solution to the asked query:

Let the number x.Now x should be a positive integer.14×x=666666x=66666614x=47619 AnswerYou can check that 66,666,6666,66666 are not divisible by 14, hence 666666 isthe smallest possible number.

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LET THE NUMBER BE X 
14X = 666 ( ASSUMED )
X = 666/14
666 IS NOT DIVISIBLE BY 14 SO IT IS NOT POSSIBLE.

14X = 6666 
X = 6666/14
6666 IS NOT DIVISIBLE BY 14 SO IT IS NOT POSSIBLE.

14X = 66666
X =  66666/14
66666 IS NOT DIVISIBLE BY 14 SO IT IS NOT POSSIBLE.

14X = 666666
X = 666666/14 
X = 47619






HENCE WHEN 14 IS MULTIPLIED BY 47619 THE ANSWER IS ENTIRELY SIXES ( 666666 )




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