Question
What is the smallest number by which 392 must be multiplied , so that the product
is a perfect cube ?
Hint:
By Factorization method we find the number by which 392 to be multiplied to
The correct answer is: 7
Explanation : prime factorize 392
392 = 2 
196
= 2 2 98
= 2 2 2 49
= 2 2 2 7 7
= 
To be a cube all the powers of prime factors should be divisible by 3.
To make 392 a cube we need to multiply it with 7 so that the power of 7 becomes 3.
Therefore,7 is the number to be multiplied to 392 to make it a cube number .
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