Two ropes measuring 45 feet and 60 feet are to be cut into equal pieces of the greatest possible length, with none left over. How long is each piece?

Correct answer to question 120 (Arithmetic Reasoning): 15 feet

Method

The piece length must divide both ropes exactly, and the longest such length is the greatest common factor. Since 45 is 3 x 3 x 5 and 60 is 2 x 2 x 3 x 5, they share 3 x 5 = 15 feet. That gives 3 pieces from one rope and 4 from the other.