Shelly and Michelle are making a quilt. They have a piece of fabric that measures 48 inches by 168 inches. All pieces must be square with none left over . What is the side length of the largest square that can be cut?
How can you have 54 inches on a side when the width of the fabric is only 48 inches?
Each square can be 24 by 24 inches.
The GCF of 128, and 48 is 24 therefore, the largest of each square she can make is 24 inches in each side
How many pieces can be cut?
Your right
To find the side length of the largest square that can be cut from a given piece of fabric, we need to find the greatest common divisor (GCD) of the two dimensions of the fabric. In this case, the dimensions are 48 inches and 168 inches.
To find the GCD, we can use the Euclidean algorithm. Here are the steps:
1. Divide the larger number (168) by the smaller number (48).
168 ÷ 48 = 3 remainder 24
2. We then divide the divisor (48) by the remainder (24).
48 ÷ 24 = 2 remainder 0
3. Since we've reached a remainder of 0, the divisor at this step (24) is the GCD.
Therefore, the GCD of 48 and 168 is 24.
The side length of the largest square that can be cut from the fabric is equal to the GCD, which is 24 inches.