A number theory problem by Manav Sinha

Number Theory Level 3

find the smallest integer k such that the product of 420 and k is a perfect square.


The answer is 105.

Manav Sinha by Manav Sinha , 20, India

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4 solutions

Nilangini Gupta
Apr 17, 2014

420 = 2^2 * 3 * 5 * 7 (prime factors)

That means, if we multiply 420 by 3 * 5 * 7 = 105, then 420*105 becomes a perfect square because

420 * 105 = 2^2 * 3^2 * 5^2 * 7^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Amit Kumar
Feb 6, 2017

420=4 15 7,so 4 comes from square root 2,and left number Sq root after multiply by same

0 Helpful 0 Interesting 0 Brilliant 0 Confused
S W
Apr 22, 2014

Prime factor is 105 and 420*105 is perfect squre

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rahul Gautam
Apr 6, 2014

420 = 2^2 3 5 7 to make this number perfect square we need 3 5*7 = 105

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