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What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube?
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Smallest Number to Multiply 2560 to Make a Perfect Cube
Understanding the Problem
- To find the smallest number by which 2560 must be multiplied to make the product a perfect cube, we need to break down 2560 into its prime factors.
Prime Factorization of 2560
- 2560 can be expressed as 2^8 * 5
Making the Product a Perfect Cube
- To make the product a perfect cube, we need to make the exponents of all prime factors multiples of 3.
- Since the exponent of 2 in 2560 is 8, it needs to be increased to the nearest multiple of 3, which is 9.
- Similarly, the exponent of 5 is already 1, which is a multiple of 3.
- Therefore, the smallest number by which 2560 must be multiplied to make it a perfect cube is 2^(9-8) * 5^(3-1) = 2 * 5^2 = 50.
Conclusion
- The smallest number by which 2560 must be multiplied to make the product a perfect cube is 50.
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What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube?
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What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube?.
What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest number by which 2560 is to be multiplied so that they product of a perfect cube?.
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