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What is the smallest positive integer k such that the produc

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Carcass
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What is the smallest positive integer k such that the produc [#permalink] New post   Updated on: 02 Feb 2020, 13:30
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What is the smallest positive integer k such that the product 1575×k is a perfect square?

(A) 7

(8) 9

(C) 15

(D) 25

(E) 63


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Originally posted by Carcass on 02 Feb 2020, 09:46.
Last edited by Carcass on 02 Feb 2020, 13:30, edited 1 time in total.
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Re: What is the smallest positive integer k such that the produc [#permalink] New post   02 Feb 2020, 11:12
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Carcass wrote:
What is the smallest positive integer k such that the product 1575∗k is a perfect square?

(A) 7

(8) 9

(C) 15

(D) 25

(E) 63


Kudos for the right answer and explanation




Let us Factorize 1575: 1575=5∗315=5∗5∗63=25∗9∗7=52∗32∗7

Since we need to make 1575∗k to become a perfect square, we need to multiply 1575 with 7 so that the resulting number has even powers of all its primes (a perfect square has even exponents of all its prime factors)

Thus, k=7

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Re: What is the smallest positive integer k such that the produc [#permalink]
02 Feb 2020, 11:12
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