Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.

To do:

We have to find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.

Solution:

Perfect Square: A perfect square has each distinct prime factor occurring an even number of times.

$28812=2\times2\times3\times7\times7\times7\times7$

$=(2)^2\times3\times(7)^2\times(7)^2$

$28812\div3=(2)^2\times3\times(7)^2\times(7)^2\div3$

$=(2\times7\times7)^2$

$=(98)^2$

In order to make the pairs an even number of pairs, we have to divide 28812 by 3, then the product will be the perfect square.

Therefore, 3 is the smallest number by which 28812 must be divided so that the quotient is a perfect square. 

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Updated on: 10-Oct-2022

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