Question

find the smallest number by which 16384 be divided so that the quotient may be a perfect cube​

Answer 1

Answer:

The quotient of a perfect cube is 4

Step-by-step explanation:

Dividend of the question =16384

Divisor=?

Prime factorization of 16384= 2×2×2×2x2x2x2x2x2x2x2x2x2x2

           $=2^{3} \times 2^{3} \times 2^{3} \times 2^{2}$

There are four $2^{3}$ if multiplied by those four $2^{3}$ i3 4

4 is the only number which is not a cube  

We take 4 from the factorization the product $2^{3}$ will be perfect cube

If 16834 is divided by 4, quotient remaining is $\left(2^{3}\right)^{4}$ =4096

The quotient of a perfect cube is 4

Answer 2

Step-by-step explanation:

Resolving 16384 into prime factors ,we get

2| 16384

___________

2| 8192

___________

2| 4096

___________

2| 2048

___________

2| 1024

___________

2| 512

___________

2| 256

___________

2| 128

___________

2| 64

___________

2| 32

___________

2| 16

___________

2| 8

____________

2| 4

____________

***2

16384 = 2×2×2×2×2×2×2×2×2×2×2×2×2×2

Here , The prime factor 2 doesn't appear in a group of three factors.

So, 16384 is not a perfect cube.

Hence , the smallest number which is to be divided to make it a perfect cube is 2×2 = 4.

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