If x a positive integer and has twelve positive factors, what is the

Question

If x a positive integer and has twelve positive factors, what is the smallest possible value of x?

A. 2048
B. 486
C. 96
D. 72
E. 60

BrentGMATPrepNow · Accepted Answer

If you're not sure how to start with this question, don't waste a ton of time searching for a solution. 
Instead,  use the answer choices to your advantage . 
We'll start with the smallest value and work our way up (since we're looking for the  smallest  possible value of x)

----------------------------
To determine the number of divisors of each answer choice, we'll use this handy trick:
If the  prime factorization  of N = (p^ a )(q^ b )(r^ c ) . . . (where p, q, r, etc are different prime numbers), then N has a total of ( a +1)( b +1)( c +1)(etc) positive divisors.

Example : 14000 = (2^ 4 )(5^ 3 )(7^ 1 )
So, the number of positive divisors of 14000 = ( 4 +1)( 3 +1)( 1 +1) =(5)(4)(2) = 40
-----------------------

E. 60
60 = (2)(2)(3)(5) = (2^ 2 )(3^ 1 )(5^ 1 )
So, the number of positive divisors of 60 = ( 2 +1)( 1 +1)( 1 +1) =(3)(2)(2) = 12

Voila!!

Answer: E

Cheers,
Brent

Archit3110 · Answer

x a positive integer and has twelve positive factors, the smallest possible value of x

IMO D ; 72 ; 2^3 * 3^2

ScottTargetTestPrep · Answer

To determine the number of positive factors of a number, we prime factorize the number and then add 1 to each prime factor’s exponent. Then we multiply those values. For example, to find the number of factors of 12, we see that the prime factorization of 12 is 2^2 x 3^1. The exponents are 2 and 1. Adding 1 to each exponent and multiplying the resulting values, we obtain (2 + 1)(1 + 1) = 3 x 2 = 6. So 12 has 6 total positive factors.

We can use the numbers in the given choices starting with the smallest.

E. 60

The prime factorization of 60 is 2^2 x 3^1 x 5^1 Therefore, 60 has (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12 factors. We see that choice E is the correct answer.

Answer: E

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If x a positive integer and has twelve positive factors, what is the

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If x a positive integer and has twelve positive factors, what is the

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