Suppose you have two similar figures, one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

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Example:
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Here, $\frac{XY}{UV}=\frac{12}{3}=4$. So, the scale factor * *is $4$.

Note that when a two-dimensional figure is enlarged (dilated) by a scale factor of $k$, the area of the figure is changed by a factor of ${k}^{2}$ . In case of three-dimensional figures, when a figure is dilated by a scale factor of $k$, the volume is changed by a factor of ${k}^{3}$.