The scale factor of a dilation is the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the preimage.

In this case, the distance from point R (the center of dilation) to each point on circle e is 2, and the distance from R to the corresponding points on circle f is 8. The scale factor $k$ is calculated as:

$k = \frac{\text{distance from R to point on circle f}}{\text{distance from R to point on circle e}} = \frac{8}{2} = 4$

Thus, the scale factor is 4.

Would you like further details on how dilation works or have any additional questions?

Here are 5 related questions to explore further:

1. What is the general effect of a dilation on the size of a geometric shape?
2. How do you find the center of dilation given two corresponding points?
3. What happens if the scale factor is less than 1 in a dilation?
4. How does the area of a shape change when it is dilated by a certain scale factor?
5. What are other transformations besides dilation that can alter the size of a figure?

Tip: The scale factor also applies to the ratio of corresponding lengths (such as radius) between the original and the dilated shape.