All I see is fours

Logic Level 2

1=44÷442=4×4÷(4+4)3=(4+4+4)÷44=4+(4×(44))5=(4+(4×4))÷4\large{\begin{aligned} 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{aligned}}

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+4444 + 44 .

Inspired by a popular recreational puzzle game.

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