If x = 6p, where p is a positive integer greater than 15

Question

If x = 6p, where p is a positive integer greater than 15, what is the
minimum possible number of factors of x?

A) 4 
B) 8 
C) 9 
D) 6
E) 12

ocelot22 · Answer

The number of factors of a integer x can be found writing the number as powers of its prime factors, adding 1 to each exponent, and multiplying the result. To find the minimum number of factors for 6p write as 2*3*p where p is assumed to be some prime factor (since a prime factor has only itself) Then the minimum number of factors for 6p is (1+1)(1+1)(1+1) = 2*2*2 = 8 B

MahmoudFawzy · Answer

To get a minimum numbers of factors of x, p should be prime (17,19,...)

so x =  2^13^1p^1  , and number of factors = (1+1)(1+1)(1+1) = 8, so  B

for more about "Finding the Number of Factors of an Integer":  https://gmatclub.com/forum/math-number-theory-88376.html

Noshad · Answer

hi  chetan2u 
I can not understand above explanation. Can you please explain this question

edlc313 · Answer

Let me give this a shot.

We know that 6 has 4 factors - 1,2,3,6. The factors of P can be found by the prime factorization. For example, 100 has a prime factorization of  2^2 * 5^2 , so that's 9 factors. We want to minimize the factors of P. Conceptually, prime numbers only have 2 factors - 1 and itself. This would give us the minimum.

So as the above post wrote, the minimum can be found by using  2^1*3^1*p^1 . That would be 8 factors (take the number in the exponents, add 1 to each, then multiply the results of each).

ScottTargetTestPrep · Answer

We want to let p = a prime number because a prime number has the fewest possible factors. So if p = 17, we see that 6 x 17 = 2^1 x 3^1 x 17^1.

To calculate the number of possible factors, we add 1 to each exponent of the prime factorization of the number and then find the product of the sums. Thus, there are (1 + 1) x (1 + 1) x (1 + 1) = 8 possible factors of x.

Answer: B

heisenberg11 · Answer

6=2*3 have 2*2=4 factors , considering only the prime value of p will give minimum number of factors i.e 2*2*2 =8 , while p can take 17,19,23...

Posted from my mobile device

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If x = 6p, where p is a positive integer greater than 15

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If x = 6p, where p is a positive integer greater than 15

Prep Toolkit

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