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Which of the following number is the product of exactly three distinct prime number?
- a)20
- b)165
- c)45
- d)147
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following number is the product of exactly three distinct...
(a) 20: Prime factorization: 20 = 2 × 2 × 5
It has only 2 distinct primes (2 and 5).
It has only 2 distinct primes (2 and 5).
(b) 165: Prime factorization: 165 = 3 × 5 × 11
It has exactly 3 distinct primes (3, 5, and 11).
It has exactly 3 distinct primes (3, 5, and 11).
(c) 45: Prime factorization: 45 = 3 × 3 × 5
It has only 2 distinct primes (3 and 5).
It has only 2 distinct primes (3 and 5).
(d) 147: Prime factorization: 147 = 3 × 7 × 7
It has only 2 distinct primes (3 and 7).
It has only 2 distinct primes (3 and 7).
The number that is the product of exactly three distinct prime numbers is: (b) 165
Most Upvoted Answer
Which of the following number is the product of exactly three distinct...
Understanding Distinct Prime Numbers
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. A number that is the product of exactly three distinct prime numbers can be represented as p1 * p2 * p3, where p1, p2, and p3 are distinct prime numbers.
Analysis of Each Option
- Option a: 20
- Prime factorization: 20 = 2 * 2 * 5
- Distinct primes: 2, 5
- Count: Only 2 distinct primes.
- Option b: 165
- Prime factorization: 165 = 3 * 5 * 11
- Distinct primes: 3, 5, 11
- Count: Exactly 3 distinct primes.
- Option c: 45
- Prime factorization: 45 = 3 * 3 * 5
- Distinct primes: 3, 5
- Count: Only 2 distinct primes.
- Option d: 147
- Prime factorization: 147 = 3 * 7 * 7
- Distinct primes: 3, 7
- Count: Only 2 distinct primes.
Conclusion
Among the options provided, only option b (165) is the product of exactly three distinct prime numbers: 3, 5, and 11. Thus, the correct answer is option 'B'.
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. A number that is the product of exactly three distinct prime numbers can be represented as p1 * p2 * p3, where p1, p2, and p3 are distinct prime numbers.
Analysis of Each Option
- Option a: 20
- Prime factorization: 20 = 2 * 2 * 5
- Distinct primes: 2, 5
- Count: Only 2 distinct primes.
- Option b: 165
- Prime factorization: 165 = 3 * 5 * 11
- Distinct primes: 3, 5, 11
- Count: Exactly 3 distinct primes.
- Option c: 45
- Prime factorization: 45 = 3 * 3 * 5
- Distinct primes: 3, 5
- Count: Only 2 distinct primes.
- Option d: 147
- Prime factorization: 147 = 3 * 7 * 7
- Distinct primes: 3, 7
- Count: Only 2 distinct primes.
Conclusion
Among the options provided, only option b (165) is the product of exactly three distinct prime numbers: 3, 5, and 11. Thus, the correct answer is option 'B'.
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Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer?.
Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following number is the product of exactly three distinct prime number?a)20b)165c)45d)147Correct answer is option 'B'. Can you explain this answer?.
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