A piece of cartolina is 60 cm by 48 cm.What is the least number of squares that can be cut from it with no material wasted?
Factor both dimensions.
60 = 2 * 2 * 3 * 5
48 = 2 * 2 * 3 * 2 * 2
The squares can be 2 by 2, 3 by 3 or 4 by 4. Which gives the "least number"?
4 by 4
To find the least number of squares that can be cut from a piece of cartolina without any material wasted, we need to determine the largest square that can be cut from it.
Step 1: Find the factors of both dimensions
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Step 2: Identify the common factors of both dimensions
- Common factors of 60 and 48: 1, 2, 3, 4, 6, 12
Step 3: Determine the largest square that can be cut
- The largest square that can be cut is the square with the side length equal to the greatest common factor (GCF) of both dimensions.
- The GCF of 60 and 48 is 12.
Step 4: Calculate the number of squares that can be cut
- To find the number of squares, divide each dimension by the side length of the largest square.
- Number of squares = (60 / 12) * (48 / 12) = 5 * 4 = 20 squares.
Therefore, the least number of squares that can be cut from a piece of cartolina measuring 60 cm by 48 cm without any material wasted is 20.
To find the least number of squares that can be cut from a piece of cartolina with no material wasted, we need to find the largest square that can fit within the dimensions of the cartolina.
Since the dimensions of the cartolina are 60 cm by 48 cm, we need to find the largest square that can fit within these dimensions. We can do this by finding the greatest common divisor (GCD) of the two dimensions.
To find the GCD of 60 and 48, we can use the Euclidean algorithm. Here are the steps:
1. Divide 60 by 48: 60 ÷ 48 = 1 with a remainder of 12.
2. Divide 48 by 12: 48 ÷ 12 = 4 with no remainder.
3. The last nonzero remainder obtained is 12.
Therefore, the GCD of 60 and 48 is 12.
Now, we can determine the dimensions of the largest square that can fit within the cartolina using the GCD. The sides of the square will be equal to the GCD, which is 12.
To calculate the least number of squares that can be cut from the cartolina, we divide the length and width of the cartolina by the side length of the square.
Length ÷ Side length = 60 ÷ 12 = 5
Width ÷ Side length = 48 ÷ 12 = 4
Therefore, we can cut 5 squares horizontally and 4 squares vertically from the cartolina, resulting in a total of 5 * 4 = 20 squares.