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If 65x = 3^2*5^2*13, which of the following is not a factor of

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Bunuel
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If 65x = 3^2*5^2*13, which of the following is not a factor of [#permalink] New post  08 Sep 2021, 04:44
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If \(65x = 3^2*5^2*13\), which of the following is not a factor of integer x?

A. 3
B. 5
C. 9
D. 13
E. 15
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Ritik0987654
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If 65x = 3^2*5^2*13, which of the following is not a factor of [#permalink] New post  08 Sep 2021, 05:23
Ans: (d) 13.

65x = (3²)*(5²)*(13)
= (5*13) (3²*5)
= 65 (3²*5)

Now,

3²*5 = (3*3*5)

The factors of 3²*5 are 3,5 and 9.

Based on the options given, 13 is not a factor of the given expression.

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sj296
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Re: If 65x = 3^2*5^2*13, which of the following is not a factor of [#permalink] New post  08 Sep 2021, 11:02
5*13*x = 3^2*5^2*13

=> x = 3^2*5

=> 3, 5, 9, 15 are factors of x

Out of the given options, 13 is not the factor of x

OA should be D
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Hunter2021
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Re: If 65x = 3^2*5^2*13, which of the following is not a factor of [#permalink] New post  07 Feb 2022, 16:07
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You can also use logic to solve the question.

The equation basically tells:
65x = 3*3*5*5*13

At the same time the prime factors for 65 are 5 and 13.

Thus, looking at the initial equation (65x = 3*3*5*5*13) we can shorten out the 5 and the 13 as they can not be part of what constitutes x.

Since a factor can always be build from the individual prime factors, the factors for x can be 3,5,9,15 but not 13.

Answer is D
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Re: If 65x = 3^2*5^2*13, which of the following is not a factor of [#permalink]
07 Feb 2022, 16:07
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