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# How many positive factors of 2^5*3^6*5^2 are perfect squares?

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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

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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

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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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