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

 

Answers (1)

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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