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If 5x^2 has two different prime factors, at most how many di
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Updated on: 14 Nov 2013, 09:26
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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
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Originally posted by suprememodelrus on 14 Nov 2013, 09:24.
Last edited by Bunuel on 14 Nov 2013, 09:26, edited 1 time in total.
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Re: If 5x^2 has two different prime factors, at most how many di
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14 Nov 2013, 13:07
suprememodelrus wrote: 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 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.
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Re: If 5x^2 has two different prime factors, at most how many di
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13 Feb 2014, 04:07
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



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Re: If 5x^2 has two different prime factors, at most how many di
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14 Jan 2017, 01:14
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.
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Re: If 5x^2 has two different prime factors, at most how many di
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22 Aug 2018, 11:47
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.
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Re: If 5x^2 has two different prime factors, at most how many di
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26 Aug 2018, 18:25
suprememodelrus wrote: 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 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
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Re: If 5x^2 has two different prime factors, at most how many di
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30 Aug 2018, 18:14
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)
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