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Consider the natural number 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 the above
Correct answer is option 'C'. Can you explain this answer?
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Consider the natural number 88935. Then the least natural number by wh...
If this no. is multiplied by 15 then it will the square of
5 × 3 × 7 × 11 = 1155
5 × 3 × 7 × 11 = 1155
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Consider the natural number 88935. Then the least natural number by wh...
Understanding Square Numbers
To determine how to make the number 88935 a perfect square, we first need to understand the prime factorization of the number.
Prime Factorization of 88935
1. Divide 88935 by small prime numbers:
- 88935 is odd (not divisible by 2).
- Sum of digits (8+8+9+3+5=33) is divisible by 3, so 88935 is divisible by 3.
- 88935 ÷ 3 = 29645.
- Next, check 29645 for divisibility by 5 (last digit is 5):
- 29645 ÷ 5 = 5929.
- Now, factor 5929:
- It is 77² (since 77 x 77 = 5929).
2. Combining these factors:
- 88935 = 3 x 5 x 77 x 77 = 3 x 5 x 7² x 11².
Identifying Perfect Square Requirements
A number is a perfect square if all the prime factors have even exponents. In our case:
- 3 has an exponent of 1 (odd).
- 5 has an exponent of 1 (odd).
- 7 has an exponent of 2 (even).
- 11 has an exponent of 2 (even).
To make it a perfect square:
- We need to multiply by 3 (to make the exponent of 3 even).
- We need to multiply by 5 (to make the exponent of 5 even).
Calculating the Least Natural Number
To achieve an even exponent for both odd primes (3 and 5):
- Multiply by 3 x 5 = 15.
Thus, the least natural number by which we can multiply 88935 to make it a perfect square is 15.
Conclusion
The correct option is C) 15.
To determine how to make the number 88935 a perfect square, we first need to understand the prime factorization of the number.
Prime Factorization of 88935
1. Divide 88935 by small prime numbers:
- 88935 is odd (not divisible by 2).
- Sum of digits (8+8+9+3+5=33) is divisible by 3, so 88935 is divisible by 3.
- 88935 ÷ 3 = 29645.
- Next, check 29645 for divisibility by 5 (last digit is 5):
- 29645 ÷ 5 = 5929.
- Now, factor 5929:
- It is 77² (since 77 x 77 = 5929).
2. Combining these factors:
- 88935 = 3 x 5 x 77 x 77 = 3 x 5 x 7² x 11².
Identifying Perfect Square Requirements
A number is a perfect square if all the prime factors have even exponents. In our case:
- 3 has an exponent of 1 (odd).
- 5 has an exponent of 1 (odd).
- 7 has an exponent of 2 (even).
- 11 has an exponent of 2 (even).
To make it a perfect square:
- We need to multiply by 3 (to make the exponent of 3 even).
- We need to multiply by 5 (to make the exponent of 5 even).
Calculating the Least Natural Number
To achieve an even exponent for both odd primes (3 and 5):
- Multiply by 3 x 5 = 15.
Thus, the least natural number by which we can multiply 88935 to make it a perfect square is 15.
Conclusion
The correct option is C) 15.
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Consider the natural number 88935. Then the least natural number by which we can divide or multiply the number to make it a square number is—a)3b)5c)15d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Consider the natural number 88935. Then the least natural number by which we can divide or multiply the number to make it a square number is—a)3b)5c)15d)None of the aboveCorrect 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 number 88935. Then the least natural number by which we can divide or multiply the number to make it a square number is—a)3b)5c)15d)None of the aboveCorrect 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 number 88935. Then the least natural number by which we can divide or multiply the number to make it a square number is—a)3b)5c)15d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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