# Q.3  Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 81(ii) 128(iii) 135(iv) 192(v) 704

D Devendra Khairwa

By prime factorization of given numbers :

(i) 81 :      $3\times3\times3\times3$

So given number needs to be divided by 3 to get a perfect cube.

(ii) 128 :    $2\times2\times2\times2\times2\times2\times2$.

So the given number needs to be divided by 2 to get a perfect cube.

(iii) 135 :    $3\times3\times3\times5$

So the given number needs to be divided by 5 to get a perfect cube.

(iv) 192 :    $2\times2\times2\times2\times2\times2\times3$

So the given number needs to be divided by 3 to get a perfect cube.

(v)  704 :    $2\times2\times2\times2\times2\times2\times11$

So the given number needs to be divided by 11 to get a perfect cube.

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