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