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39 votes
39 votes
¿Cuál es el número positivo más pequeño que se puede sumar a 55 para que el número resultante y 45 tengan 9 como su máximo factor común? 5 or 8 or 9 or 17

User Mark Giaconia
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1 Answer

12 votes
12 votes

So we need a number x such that 55+x and 45 have 9 as gcd. The multiples of 9 are


\begin{gathered} 9, \\ 18, \\ 27, \\ 36, \\ 45, \\ 54, \\ 63, \\ \ldots \end{gathered}

Then, the next multiple of 9 after 55 is 63, so if we add x=8 to 55, then


\begin{gathered} 63=7*9 \\ 45=5*9 \end{gathered}

63 and 45 have 9 as their gcd. Then the answer is x=8.

User Aaron Averett
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