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What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght?
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What is the least possible number of planks,if three pieces of timber ...
The least possible number of planks is determined by the greatest common factor (GCF) of the three timber lengths. The GCF of 42, 49, and 63 can be found by first finding the prime factorization of each number:
42 = 2 * 3 * 749 = 7 * 763 = 3 * 3 * 7
The GCF is the product of the common prime factors, which in this case is 7. Therefore, the least possible number of planks is 7.
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What is the least possible number of planks,if three pieces of timber ...
Calculating the least number of planks
The first step in determining the least number of planks is to find the greatest common divisor (GCD) of the lengths of the three pieces of timber.
Finding the GCD
- The lengths of the timber pieces are 42m, 49m, and 63m.
- The GCD of these three numbers is 7m.
Calculating the number of planks
- To find the least possible number of planks, we need to divide each length by the GCD.
- 42m ÷ 7m = 6 planks
- 49m ÷ 7m = 7 planks
- 63m ÷ 7m = 9 planks
Final answer
- The least possible number of planks that can be cut from the three timber pieces is 7 planks.
- This is because each piece can be divided into a whole number of planks equal to the length of the timber divided by the GCD.
The first step in determining the least number of planks is to find the greatest common divisor (GCD) of the lengths of the three pieces of timber.
Finding the GCD
- The lengths of the timber pieces are 42m, 49m, and 63m.
- The GCD of these three numbers is 7m.
Calculating the number of planks
- To find the least possible number of planks, we need to divide each length by the GCD.
- 42m ÷ 7m = 6 planks
- 49m ÷ 7m = 7 planks
- 63m ÷ 7m = 9 planks
Final answer
- The least possible number of planks that can be cut from the three timber pieces is 7 planks.
- This is because each piece can be divided into a whole number of planks equal to the length of the timber divided by the GCD.
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What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght?.
What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least possible number of planks,if three pieces of timber 42m 49m and 63m long have been divided into planks of same lenght?.
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