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What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?
- a)2
- b)5
- c)7
- d)11
Correct answer is option 'C'. Can you explain this answer?
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What is the least prime number by which 2800 should be multiplied so t...
Prime Factorization of 2800:
- To find the least prime number by which 2800 should be multiplied to get a perfect square, first, we need to find the prime factorization of 2800.
- Prime factorization of 2800 is 2^4 * 5^2 * 7.
Finding the Missing Prime Factor:
- To make the product a perfect square, we need to have an even power of each prime factor in the factorization.
- In the prime factorization of 2800, the exponent of 7 is 1. To make it a perfect square, we need to multiply it by 7.
- Therefore, the least prime number by which 2800 should be multiplied is 7.
Verification:
- When we multiply 2800 by 7, we get 19600.
- The prime factorization of 19600 is 2^4 * 5^2 * 7^2, which is a perfect square as each prime factor has an even power.
Therefore, the correct answer is option 'c) 7'.
- To find the least prime number by which 2800 should be multiplied to get a perfect square, first, we need to find the prime factorization of 2800.
- Prime factorization of 2800 is 2^4 * 5^2 * 7.
Finding the Missing Prime Factor:
- To make the product a perfect square, we need to have an even power of each prime factor in the factorization.
- In the prime factorization of 2800, the exponent of 7 is 1. To make it a perfect square, we need to multiply it by 7.
- Therefore, the least prime number by which 2800 should be multiplied is 7.
Verification:
- When we multiply 2800 by 7, we get 19600.
- The prime factorization of 19600 is 2^4 * 5^2 * 7^2, which is a perfect square as each prime factor has an even power.
Therefore, the correct answer is option 'c) 7'.
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Community Answer
What is the least prime number by which 2800 should be multiplied so t...
Multiply 7 x 2800 = 19600
Which is square of 140
Which is square of 140
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What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer?
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What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer?.
What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least prime number by which 2800 should be multiplied so that the product may be a perfect square?a)2b)5c)7d)11Correct answer is option 'C'. Can you explain this answer?.
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