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The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly?
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The length breadth and height of a room are 825cm 675cm and450cm respe...
Understanding the Problem
To find the longest tape that can measure the room's dimensions exactly, we need to determine the greatest common divisor (GCD) of the room's length, breadth, and height.
Room Dimensions
- Length: 825 cm
- Breadth: 675 cm
- Height: 450 cm
Step 1: Find the Prime Factors
- 825:
- Prime factorization: 3 × 5 × 5 × 11 (or 3 × 5^2 × 11)
- 675:
- Prime factorization: 3 × 3 × 5 × 5 (or 3^2 × 5^2)
- 450:
- Prime factorization: 2 × 3 × 3 × 5 × 5 (or 2 × 3^2 × 5^2)
Step 2: Identify Common Factors
Now, we look for common prime factors among the numbers:
- Common Factors:
- 3 appears at least twice in each factorization.
- 5 appears at least twice in each factorization.
Step 3: Calculate the GCD
The GCD is found by taking the lowest power of the common prime factors:
- GCD = 3^2 × 5^2 = 9 × 25 = 225 cm.
Conclusion
The longest tape that can measure the three dimensions of the room exactly is 225 cm. This tape can measure all dimensions without any leftover length.
To find the longest tape that can measure the room's dimensions exactly, we need to determine the greatest common divisor (GCD) of the room's length, breadth, and height.
Room Dimensions
- Length: 825 cm
- Breadth: 675 cm
- Height: 450 cm
Step 1: Find the Prime Factors
- 825:
- Prime factorization: 3 × 5 × 5 × 11 (or 3 × 5^2 × 11)
- 675:
- Prime factorization: 3 × 3 × 5 × 5 (or 3^2 × 5^2)
- 450:
- Prime factorization: 2 × 3 × 3 × 5 × 5 (or 2 × 3^2 × 5^2)
Step 2: Identify Common Factors
Now, we look for common prime factors among the numbers:
- Common Factors:
- 3 appears at least twice in each factorization.
- 5 appears at least twice in each factorization.
Step 3: Calculate the GCD
The GCD is found by taking the lowest power of the common prime factors:
- GCD = 3^2 × 5^2 = 9 × 25 = 225 cm.
Conclusion
The longest tape that can measure the three dimensions of the room exactly is 225 cm. This tape can measure all dimensions without any leftover length.
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The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly?
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The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly?.
The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length breadth and height of a room are 825cm 675cm and450cm respectively find the longest tape which can measure the three dimensions of the room exactly?.
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