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How many positive factors of 2^5*3^6*5^2 are perfect squares? [#permalink]
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Bunuel wrote:
How many positive factors of \(2^5*3^6*5^2\) are perfect squares?

A. 8
B. 12
C. 18
D. 24
E. 36


Are You Up For the Challenge: 700 Level Questions


Solution:


    • \(2^5*3^6*5^2\)
      o We need to find the factors of the above number which are perfect square.
      o We need to the factors with even power for this.
    • \(2^5\) has 3 factors with even power i.e., \(2^0, 2^2\), and \(2^4\).
    • \(3^6\) has 4 factors with even power i.e., \(3^0, 3^2, 3^4,\) and \(3^6\)
    • \(5^2\) has two factors with even power i.e., \(5^0\) and \(5^2\)
      o Required number = \(3*4*2 = 24\).
Hence, the correct answer is Option D.­
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How many positive factors of 2^5*3^6*5^2 are perfect squares? [#permalink]
pair of square of \(2^5*3^6*5^2\)

(2^2)^2 * (3^2)^3 * (5^2)^1 * 2
factors of squares ; 3*4*2 ; 24
OPTION D

Bunuel wrote:
How many positive factors of \(2^5*3^6*5^2\) are perfect squares?

A. 8
B. 12
C. 18
D. 24
E. 36


Are You Up For the Challenge: 700 Level Questions

­
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Re: How many positive factors of 2^5*3^6*5^2 are perfect squares? [#permalink]
How many positive factors of 2^5∗3^6∗5^2 are perfect squares?

Any factor of 2^5∗3^6∗5^2 which is a perfect square will be of the form 2^a∗3^b∗5^c where
a can be 0 or 2 or 4 (3 ways)
b can be 0 or 2 or 4 or 6 (4 ways)
c can be 0 or 2 (2 ways)
so,required number of factors=3×4×2=24

correct answer D
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Re: How many positive factors of 2^5*3^6*5^2 are perfect squares? [#permalink]
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Re: How many positive factors of 2^5*3^6*5^2 are perfect squares? [#permalink]
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