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By what least number should we multiply 1008 to make it a perfect square?
- a)8
- b)7
- c)2
- d)5
Correct answer is option 'B'. Can you explain this answer?
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To find the least number by which we should multiply 1008 to make it a perfect square, we need to factorize 1008 and then identify the missing prime factors.
Factorizing 1008:
The prime factorization of 1008 can be found by dividing it by prime numbers starting from 2.
1008 ÷ 2 = 504
504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
Hence, the prime factorization of 1008 is 2 × 2 × 2 × 2 × 3 × 7.
Identifying the missing prime factors:
To make 1008 a perfect square, we need to have an even number of each prime factor.
From the factorization, we can see that we have four 2's, one 3, and one 7. To make the number of 2's even, we need to multiply 1008 by another 2.
So, the least number by which we should multiply 1008 to make it a perfect square is 2.
Conclusion:
To make 1008 a perfect square, we need to multiply it by 2. Therefore, the correct answer is option B) 2.
Factorizing 1008:
The prime factorization of 1008 can be found by dividing it by prime numbers starting from 2.
1008 ÷ 2 = 504
504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
Hence, the prime factorization of 1008 is 2 × 2 × 2 × 2 × 3 × 7.
Identifying the missing prime factors:
To make 1008 a perfect square, we need to have an even number of each prime factor.
From the factorization, we can see that we have four 2's, one 3, and one 7. To make the number of 2's even, we need to multiply 1008 by another 2.
So, the least number by which we should multiply 1008 to make it a perfect square is 2.
Conclusion:
To make 1008 a perfect square, we need to multiply it by 2. Therefore, the correct answer is option B) 2.
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By what least number should we multiply 1008 to make it a perfect square?a)8b)7c)2d)5Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about By what least number should we multiply 1008 to make it a perfect square?a)8b)7c)2d)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for By what least number should we multiply 1008 to make it a perfect square?a)8b)7c)2d)5Correct answer is option 'B'. Can you explain this answer?.
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