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Consider the natural numbers 88935. Then the least natural number by which we can divide or multiply the number to make it a square number is
- a)3
- b)5
- c)15
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the natural numbers 88935. Then the least natural number by w...
88935 can be written as 5929 x 15
5929 is the square of 77
So, the answer is 15
Most Upvoted Answer
Consider the natural numbers 88935. Then the least natural number by w...
Understanding Square Numbers
A square number is defined as a number that can be expressed as the square of an integer. For a natural number to be a square, all prime factors must have even powers.
Prime Factorization of 88935
To find the least number by which we can divide or multiply 88935 to make it a square number, we first perform prime factorization.
- 88935 is divisible by 3:
- 88935 ÷ 3 = 29645
- Next, 29645 is divisible by 5:
- 29645 ÷ 5 = 5929
- Finally, we find that 5929 is 77 squared (7 * 11).
Thus, the prime factorization of 88935 is:
- 3^1 * 5^1 * 7^2 * 11^2
Analyzing Prime Factors
From the prime factorization, we can observe the powers of each prime factor:
- The power of 3 is 1 (odd)
- The power of 5 is 1 (odd)
- The power of 7 is 2 (even)
- The power of 11 is 2 (even)
In order to make 88935 a square number, we need to adjust the odd powers.
Required Adjustments
To convert the odd powers to even:
- For 3: We need to multiply by 3 (to make it 2)
- For 5: We need to multiply by 5 (to make it 2)
To find the least number to multiply to make all powers even, we can multiply by both 3 and 5:
- 3 * 5 = 15
Conclusion
Thus, the least natural number by which we can multiply 88935 to make it a square number is 15.
Therefore, the correct answer is option 'C'.
A square number is defined as a number that can be expressed as the square of an integer. For a natural number to be a square, all prime factors must have even powers.
Prime Factorization of 88935
To find the least number by which we can divide or multiply 88935 to make it a square number, we first perform prime factorization.
- 88935 is divisible by 3:
- 88935 ÷ 3 = 29645
- Next, 29645 is divisible by 5:
- 29645 ÷ 5 = 5929
- Finally, we find that 5929 is 77 squared (7 * 11).
Thus, the prime factorization of 88935 is:
- 3^1 * 5^1 * 7^2 * 11^2
Analyzing Prime Factors
From the prime factorization, we can observe the powers of each prime factor:
- The power of 3 is 1 (odd)
- The power of 5 is 1 (odd)
- The power of 7 is 2 (even)
- The power of 11 is 2 (even)
In order to make 88935 a square number, we need to adjust the odd powers.
Required Adjustments
To convert the odd powers to even:
- For 3: We need to multiply by 3 (to make it 2)
- For 5: We need to multiply by 5 (to make it 2)
To find the least number to multiply to make all powers even, we can multiply by both 3 and 5:
- 3 * 5 = 15
Conclusion
Thus, the least natural number by which we can multiply 88935 to make it a square number is 15.
Therefore, the correct answer is option 'C'.
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Consider the natural numbers 88935. Then the least natural number by which we can divide or multiply the number to make it a square number isa)3b)5c)15d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Consider the natural numbers 88935. Then the least natural number by which we can divide or multiply the number to make it a square number isa)3b)5c)15d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Consider the natural numbers 88935. Then the least natural number by which we can divide or multiply the number to make it a square number isa)3b)5c)15d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the natural numbers 88935. Then the least natural number by which we can divide or multiply the number to make it a square number isa)3b)5c)15d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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