Is it possible to divide 1,000 into two parts | vedclass

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(D) Let the two parts be $15x$ and $15y$,where $x$ and $y$ are coprime integers.Their sum is $15x + 15y = 1000$.Dividing by $15$,we get $x + y = 1000

Vedclass · Accepted Answer

Never possible

Vedclass · Answer

(D) Let the two parts be $15x$ and $15y$,where $x$ and $y$ are coprime integers.Their sum is $15x + 15y = 1000$.Dividing by $15$,we get $x + y = 1000 / 15 = 200 / 3$.Since $x$ and $y$ must be integers,their sum $x + y$ must also be an integer.However,$200 / 3$ is not an integer $(66.66...)$.Therefore,it is not possible to divide $1000$ into two parts such that their $HCF$ is $15$.Hence,the correct answer is $(d)$.

Is it possible to divide $1,000$ into two parts such that their $HCF$ is $15$?

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