# A number when divided by a divisor leaves 27 as remainder Twice the number when divided by the same number leaves remainder 3.Find the divisor. Please explain.Thanks

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by Wonderer09

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by Wonderer09

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The 2 equations formed are:

1) num=d*q1+27

2)2*num=d*q2+3

Multiplying equation-1 by 2 and equating the equations gives us

=>d*q2+3=2dq1+54

Shifting the d term on one side and numbers on the other

=>d*q2-2*q1=51

Taking d common from the left side

=>d(q2-2q1)=51

=>d=51/q2-2*q1

So d can either be 51 or one of its factor(17 or 3)