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Hi Roland2rule,In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?
A. 2
B. 3
C. 5
D. 6
E. 8
OA is B
Which option is correct, OA says B. But I got E. Pls an Expert should help out.
Let's take a look at your question.
N is a positive integer less than 200, and 14N/60 is an integer.
$$\frac{14N}{60}=\frac{7N}{30}$$
N must be a multiple of 30 for 7N/30 to be an integer.
Also N<200, therefore, we can only consider multiples of 300 less than 200, i.e.
$$30\times1,\ 30\times2,\ 30\times3,\ 30\times4,\ 30\times5,\ 30\times6$$
$$\text{Factors of 30}\ =\ 1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30$$
Prime factors for all possibles multiples of 30 will be 2, 3, 5.
Hence, N has 3 possible prime factors.
Therefore, Option B is correct.
Hope it helps.
I am available if you'd like any follow up.
