Question

A room measures 150cm by 90cm.Find the size of the largest square tile that can be used to tile the floor without any cutting.

Answer 1

To find the largest square tile that can be used to tile the floor without cutting, find the greatest common factor (GCF) of the length and width of the room. In this case, the GCF is 30cm, so the largest square tile measures 30cm by 30cm.

Step-by-step explanation:

To find the largest square tile that can be used to tile the floor without cutting, we need to find the greatest common factor (GCF) of the length and width of the room. In this case, the length is 150cm and the width is 90cm.

1. First, prime factorize the length and width of the room:
   • 150cm = 2 * 3 * 5 * 5
   • 90cm = 2 * 3 * 3 * 5
2. Next, find the GCF by taking the common factors with the lowest exponent:
   • GCF = 2 * 3 * 5 = 30cm

Therefore, the largest square tile that can be used to tile the floor without cutting measures 30cm by 30cm.