Kennedy plans to completely cover the wall behind her kitchen sink with square tiles. The wall is a rectangle that is 15 in. high and 24 in. long. Each square tile will have whole-number side lengths. What is the side length of the largest square tile that Kennedy can use?
The side length of the tile must divide both 15 in. and 24 in.
List the factors of 15: 1, 3, 5, 15
List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The only whole numbers that divide into both 15 and 24 are 1 and 3. The greatest common factor of 15 and 24 is 3.
The side length of the largest tile Kennedy can use is 3 in.
1
Suppose the wall in the Example is 16 in. high and 28 in. long.
a. What is the side length of the largest square tile that Kennedy can use?
b. How many tiles does Kennedy need to completely fill the wall? Show your work.
Answers
Answer:
Kennedy plans to completely cover the wall behind her kitchen sink with square tiles. The wall is a rectangle that is 15 in. high and 24 in. long. Each square tile will have whole-number side lengths. What is the side length of the largest square tile that Kennedy can use?
The side length of the tile must divide both 15 in. and 24 in.
List the factors of 15: 1, 3, 5, 15
List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The only whole numbers that divide into both 15 and 24 are 1 and 3. The greatest common factor of 15 and 24 is 3.
The side length of the largest tile Kennedy can use is 3 in.
1
Suppose the wall in the Example is 16 in. high and 28 in. long.
a. What is the side length of the largest square tile that Kennedy can use?
b. How many tiles does Kennedy need to completely fill the wall? Show