Which number should replace both the question marks in the following equation ?

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Question

Which number should replace both the question marks in the following equation ?
$$\frac{?}{{1776}} = \frac{{111}}{?}$$

Answer: Option E
$$\eqalign{
& {\text{Let }}\frac{x}{{1776}} = \frac{{111}}{x} \cr
& {\text{Then, }} \cr
& \Leftrightarrow {x^2} = 111 \times 1776 \cr
& \Leftrightarrow {x^2} = 111 \times 111 \times 16 \cr
& \Leftrightarrow x = \sqrt {{{\left( {111} \right)}^2} \times {{\left( 4 \right)}^2}} \cr
& \Leftrightarrow x = 111 \times 4 \cr
& \Leftrightarrow x = 444 \cr} $$

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