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If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?
- a)2
- b)3
- c)5
- d)6
- e)cannot be determined
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
If N is a positive integer and 14N/60 is an integer, then N has how ma...
The given condition states that 14N/60 is an integer. We can simplify this expression further:
14N/60 = 7N/30
For 7N/30 to be an integer, N must have prime factors that cancel out the prime factors in the denominator, which are 2 and 5.
If N has additional prime factors other than 2 and 5, they would not affect the divisibility by 30 since 7N/30 can still be an integer. Therefore, the number of different positive prime factors of N cannot be determined.
Hence, the correct answer is option E: cannot be determined.
Most Upvoted Answer
If N is a positive integer and 14N/60 is an integer, then N has how ma...
The given condition states that 14N/60 is an integer. We can simplify this expression further:
14N/60 = 7N/30
For 7N/30 to be an integer, N must have prime factors that cancel out the prime factors in the denominator, which are 2 and 5.
If N has additional prime factors other than 2 and 5, they would not affect the divisibility by 30 since 7N/30 can still be an integer. Therefore, the number of different positive prime factors of N cannot be determined.
Hence, the correct answer is option E: cannot be determined.
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If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?a)2b)3c)5d)6e)cannot be determinedCorrect answer is option 'E'. Can you explain this answer?
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