Question

The smallest number by which 256 must be divided so that the quotient is a perfect cube is

Answer 1

ANSWER:

• The smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.

GIVEN:

• Number = 256

TO FIND:

• Smallest number by which 256 must be divided so that the quotient is a perfect cube.

SOLUTION:

Finding the prime factorisation of 256 :

=> 256 = 2×2×2×2×2×2×2×2

Making Triplet of prime factorisation of 256.

=> 256 = (2×2×2)×(2×2×2)×2×2

Here we see that 2*2 left ungrouped so we much divide 256 by (2×2 = 4) so to get a perfect cube.

= 256/4

= 64

So the Smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.

=> 64 = (4)³

NOTE:

• This type of questions can be solved by finding the prime Factorisation of the given number.
• Then we simply according to the Question.

Answer 2

Answer:

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