A living room measures 450cm by 330cm.Find the dimension of the largest tile that can be used to tile the floor without cutting.
30
To find the dimension of the largest tile that can be used to tile the floor without cutting, we need to find the greatest common divisor (GCD) of the length and width of the room.
Step 1: Determine the GCD of 450 and 330.
To find the GCD, we can use the Euclidean algorithm:
Divide 450 by 330: 450 ÷ 330 = 1 remainder 120
Divide 330 by 120: 330 ÷ 120 = 2 remainder 90
Divide 120 by 90: 120 ÷ 90 = 1 remainder 30
Divide 90 by 30: 90 ÷ 30 = 3 remainder 0
The last non-zero remainder is 30.
Step 2: The GCD of 450 and 330 is 30.
The largest tile that can be used to tile the floor without cutting is a square tile with dimensions 30 cm by 30 cm.
To find the largest tile that can be used to tile the floor without cutting, we need to find the greatest common divisor (GCD) of the lengths of the room.
To find the GCD of two numbers, we can use the Euclidean algorithm. Here's how you can calculate it:
1. Start with the two dimensions of the room: 450cm and 330cm.
2. Divide the larger number by the smaller number and find the remainder.
- 450 ÷ 330 = 1 with a remainder of 120.
3. Now, divide the smaller number (330) by the remainder (120) from the previous step.
- 330 ÷ 120 = 2 with a remainder of 90.
4. Repeat the previous step by dividing the previous remainder (120) by the new remainder (90).
- 120 ÷ 90 = 1 with a remainder of 30.
5. Continue this process until the remainder becomes zero.
- 90 ÷ 30 = 3 with no remainder.
- 30 ÷ 0 = Undefined (since the remainder is zero).
At this point, we know that the GCD of 450cm and 330cm is the last non-zero remainder, which is 30cm.
Therefore, the largest tile that can be used to tile the living room without cutting is a square tile with dimensions of 30cm by 30cm.
Factor each dimension.
450 = 5 * 2 * 5 * 3 * 3
330 = 5 * 2 * 3 * 11
What are the common factors?