To determine the scale factor, we can use the ratio of the width of the original picture to the width of the reduced copy.
The scale factor is equal to the ratio of the size of the original image to the size of the reduced image.
In this case, the width of the original image is 5.1 inches, and the width of the reduced image is 1.6 inches. Therefore, the scale factor is:
scale factor = width of original image / width of reduced image
scale factor = 5.1 inches / 1.6 inches
scale factor = 3.1875
So, the family should reduce the picture by a scale factor of approximately 3.19 in order to fit it into a space that is 1.6 inches wide.