All I see is fours

Logic Level 2

\[\large{\begin{eqnarray} 1 &=& 44 \div 44 \\ 2 &=& 4 \times 4 \div (4 + 4 ) \\ 3 &=& (4 + 4 + 4) \div 4 \\ 4 &=& 4 + (4\times(4-4)) \\ 5 &=& (4 + (4\times4)) \div 4 \end{eqnarray}} \]

Above shows the first 5 positive integers formed by using the four mathematical operators (\(+ \ - \ \times \ \div\)) only on the digit 4 four times.

What is the smallest positive integer that cannot be represented using these conditions?

Note: You are allowed to join the digits together: \(44 + 44 \).

Inspired by a popular recreational puzzle game.

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