To increase by a factor is to multiply a magnitude by the given factor.
For example, increasing a line by a factor of 10, is to multiply the length of the line times 10.
When you want to increase the size of a picture by a factor you have to multiply both dimensions length and width by the same factor.
For example to increase the size of a picture that is 3" x 4" by a factor of 5, you will get a copy that is 15" x 20".