Question

4. The students in an art class have blue cloth that is 60 inches long, gold cloth that is 48 inches long, and white cloth that is 72 inches long. They want to cut all the cloth into pieces of equal length for a project. a. What is the greatest possible length of the pieces without having any cloth left over? Explain your reasoning. b. How many pieces of each color cloth will they have?

Answer 1

a. The greatest possible length is 12 inches as it is the greatest common factor of the three given lengths.

b. There will be 5 pcs of blue cloth, 4 pcs of gold cloth, and 6 pieces of white cloth.

Explanation:

a. What is the greatest possible length of the pieces without having any cloth left over?

Find the greatest common factor for the 3 lengths

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The greatest common factor amongst the three given lengths is 12 therefore it is also the greatest possible length.

b. Divide each length by 12.

60/12 = 5pcs ---blue cloth

48/12 = 4pcs ---gold cloth

72/12 = 6 pcs ---white cloth