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The scale factor between two similar shapes is the ratio of the dimensions of one (often the smaller) compared with the dimension of the other (the larger).
Take the 'reciprocal' of the given scale factor to go the other way. The 'reciprocal' of a number is 1/(the number). 3 ==> 1/3 5 ==> 1/5 1/7 ==> 7 2/3 ==> 3/2 etc.
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If you know one of the sides of both the rectangles than you just divide them by one another to find the scale factor.