Cut squares out of rectangular paper

I take squares out of the rectangular paper of which width is longer than length.

I take squares as many as possible whose one side is the shorter one of the rectangular paper first(Fig. 1).

If paper remains, I take squares as many as possible whose one side is the shorter one of the rectangular paper remained(Fig. 2).

This work is repeated and I finish the work when there is no remainder of the paper(Fig. 3).

(1) In the example when the length of the first rectangle is 16 cm in length, find the horizontal length.

(2) How many squares can be taken from the rectangle with 5 cm in length and 18.6 cm in width?

(3) When the length of the first rectangle shall be 10 cm in length, how many kinds of length considered as horizontal length is there in order to take five squares exactly?

Answer