In GCSE Mathematics, and the topic of transformations, specifically enlargements, the scale factor is the number that you multiply each dimension of a shape by. A scale factor greater than 1 will increase each side length; between 0 and 1, it will decrease each side length.
The original shape (object) and enlarged shape (image) will be mathematically similar. As well as working with enlargements, understanding scale factors allows us to solve problems involving the (unknown) side lengths of similar shapes.
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