Question

practice finding the greatest common factor of two whole numbers
study the example showing how to find the greatest common factor of two whole numbers. then solve problems 1 - 4.
example
the wall behind keles kitchen sink is a rectangle that is 15 in. high and 24 in. long. kele and his stepmom plan to completely cover the wall using identical square tiles with whole - number side lengths. what is the side length of the largest square tile that they 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 kele and his stepmom can use is 3 in.
a. suppose the wall in the example is 16 in. high and 28 in. long. what is the side length of the largest square tile that kele and his stepmom can use to completely cover the wall? show your work.
16: 32, 48, 64, 80, 86, 102, 118, 134, 15
28: 56, 84, 112, 140, 168, 196, 224
tion
he tile size you found in problem 1a. how many tiles do kele and his nom need to completely cover the 16 in. - by - 28 in. wall? show your wor

Explanation:

Step1: List factors of 16

Factors of 16: \(1, 2, 4, 8, 16\)

Step2: List factors of 28

Factors of 28: \(1, 2, 4, 7, 14, 28\)

Step3: Find common factors

Common factors of 16 and 28: \(1, 2, 4\)

Step4: Determine GCF

The greatest common factor (GCF) is \(4\)

Answer:

The side length of the largest square tile is \(4\) inches.