Definition
Scale factor
A scale factor is the multiplier used on every corresponding length in a scaled figure.
What it means
Match a length on the first figure with the same length on the second. One multiply-by number must work for every matching pair. That number is the scale factor. A factor of 3 makes each length three times as long; a factor of 1/2 makes each length half as long. Direction matters: from a smaller figure to a larger one the factor might be 3, while the reverse factor is 1/3.
Remember it
One figure, one multiplier, every matching length.
Example
A rectangle is 2 cm by 3 cm. A similar rectangle is 6 cm by 9 cm. Since 6 ÷ 2 = 3 and 9 ÷ 3 = 3, the scale factor from the first rectangle to the second is 3.
Watch for
Changing only one side does not make a scaled copy. Every corresponding length must use the same factor.
Common mix-up
A scale factor is not the numbered scale on a graph, a map scale, or a weighing scale. Here it is the multiplier between corresponding lengths.
Exact meaning
In the geometry and scale-drawing sense, a scale factor is the positive number k for which each image length equals k times its corresponding original length. A factor greater than 1 enlarges, a factor between 0 and 1 reduces, and a factor of 1 keeps the same size.