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If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?
- a)30
- b)60
- c)180
- d)210
- e)cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If N is a positive integer and 14N/60 is an integer. What is the small...
To find the smallest value of N with exactly four different prime factors, we need to consider the given conditions.
We are given that 14N/60 is an integer. Let's simplify this expression:
14N/60 = N/5
Since N/5 is an integer, it means that N must be a multiple of 5. Let's substitute N = 5M, where M is an integer, into the expression:
N/5 = (5M)/5 = M
So, we have reduced the problem to finding the smallest value of M that has exactly four different prime factors.
Now, let's analyze the answer choices:
A) 30 = 5 × 2 × 3, has three prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
Option C and D both have four prime factors, but we are looking for the smallest value. Hence, the correct answer is option D) 210.
Thus, the smallest value of N that satisfies the conditions and has exactly four different prime factors is 210.
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Community Answer
If N is a positive integer and 14N/60 is an integer. What is the small...
To find the smallest value of N with exactly four different prime factors, we need to consider the given conditions.
We are given that 14N/60 is an integer. Let's simplify this expression:
14N/60 = N/5
Since N/5 is an integer, it means that N must be a multiple of 5. Let's substitute N = 5M, where M is an integer, into the expression:
N/5 = (5M)/5 = M
So, we have reduced the problem to finding the smallest value of M that has exactly four different prime factors.
Now, let's analyze the answer choices:
A) 30 = 5 × 2 × 3, has three prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
Option C and D both have four prime factors, but we are looking for the smallest value. Hence, the correct answer is option D) 210.
Thus, the smallest value of N that satisfies the conditions and has exactly four different prime factors is 210.
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If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?a)30b)60c)180d)210e)cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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