Perfect Square k=?

Number Theory Level 2

What is the smallest positive integer k k such that 396 × k 396 \times k is a perfect square?


The answer is 11.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Tom Engelsman
Jan 21, 2018

The prime factorization of 396 396 computes to 2 2 3 2 1 1 1 2^{2} 3^{2} 11^{1} , which the smallest required integer is k = 11 . \boxed{k = 11}.

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Nice solution. Thank you for sharing it.

Hana Wehbi - 3 years, 4 months ago

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My pleasure, Hana!!! Stay warm during that Floridian Freeze :)

tom engelsman - 3 years, 4 months ago

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Thank you :)

Hana Wehbi - 3 years, 4 months ago

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