If 5x^2 has two different prime factors, at most how many di

Question

If 5x^2 has two different prime factors, at most how many different prime factors does x have?

(A) 1 
(B) 2 
(C) 3 
(D) 4 
(E) 5

Bunuel · Accepted Answer

x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.

Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors).

Answer: B.

stonecold · Answer

Properties in action-> 
1->When we multiply a positive integer x with another positive integer n,the number of prime factors of nx may be equal to x or greater than x.
2-> X  and  X^n  always have the exact same prime factors.
Case 1
In this case since 5x^2 has 2 prime factors.
So x can have one prime factors => and that will not be 5 so that 5x^2 has two primes.
OR
Case 2
In this case x can have two prime factors including 5 => e.g => x=5*3 => 5x^2=> 2 prime factors.
Hence At the most -> x can have 2 prime factors.

Hence B.

sgangs · Answer

A little bit more explaination:
5x^2 has 2 prime factors.
One of them has to be 5 (since 5 is a factor of 5x^2 and 5 is prime).

Since the question asks for maximum no of prime factors that x can have, the answer has to be 2 (One of the two prime nos has to be 5, like x can be 10 or 15 or 20 ...etc, with 5 along with 2 0r 3 as the other prime factor)
The other factor is not known to us.

Moreover, since the question says 5x^2 has two different prime factors, x must have atleast one factor other than 5

Seryozha · Answer

The tricky moment here is to notice that (5x)^2 has two  different  prime factors. The author does not mention the real number of prime factors. For example, the number 100 = 2*2*5*5, so has 4 prime factors, but it only has 2 distinct prime factors, 5 and 2. 
So in this question, x can have the maximum of 2 prime factors, one can be something like 2,3,7 and the other 5 to maximize the possibilities of having prime factors.

ScottTargetTestPrep · Answer

Since 5x^2 has two different prime factors, and one of them is 5, then x can have only one prime other than 5. For instance, if x = 10, then 5x^2 = 5*100 = 500; which has two prime factors, namely 2 and 5. So x can have at most two prime factors, i.e., 5 and some other prime

Answer: B

Blackishmamba · Answer

X^2 is just a X multiplied by itself.
So it won't increase / decrease the number of prime factors.

for e.g 6 (6=2x3) has two prime factors 
36 (36=2x2x3x3) also has two prime factors

Thus, # of prime factors always remains same for x, and x^2

Now coming to the question
5*X^2 has 2 prime factors
Thus 5*X will also have 2 prime factors
So, X can have at most 2 prime factors ( one of which'd be 5)

MathRevolution · Answer

5 x^2  has two different prime factors.

=> 'x' can take any value of prime factor-like 2, 3, 7 so we have 1 prime factor for x.

=> 'x' can also have prime factor '5'. x^2  still have 2 different prime factors].

Answer B

Sabby · Answer

Hi,

5x^2 has two different prime factors,therefore x could be 5*3^2 and x can at most have 2 different prime factors.

Answer B)

findingmyself · Answer

How I did it fast and quick.

Step 1: 1 Factor is 5 and is given in the question stem itself.
Step 2: Plug any square which is non prime let's say 9^2.

Evaluation of 5*9^2 shows you that for the number 5x^2 to have two diff prime factors, then the only possibility is that x^2 can be factorized into a unique prime number.(In other words, X has to be a square of prime number) Here in case 9^2 is 3*3*3*3. If we take any other number and do a square, we won't get exactly two diff factors.

Lets take 16 as X and see. 5*12^2= 5*2*2*3*2*2*3--> we can see our condition of 2 diff factors won't stand.
X^2 can thus be numbers like=9,16,25,36

ManifestDreamMBA · Answer

5x^2 has 2 different factors, is equivalent to 5x has 2 different factors. Now x can have a prime number  
eq 5   or can have a prime number * 5
For e.g. x can be 7 (1 factor) or 35 (2 factors). In both scenarios 5x or 5x^2 will have 2 factors only
At most x can have 2 factors

If 5x^2 has two different prime factors, at most how many di

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If 5x^2 has two different prime factors, at most how many di

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