Question

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

Answer 1

Answer:

16384 should be divided by 4 so that the quotient becomes a perfect cube i.e.4096 = 16^3

Answer 2

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Number = 16384

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• Find the smallest number by which 16384 can be divided so that the quotient may be perfect cube.

${\green{\underline{\underline{\bold{Solution:-}}}}}$

The dividend of the question is 16384

The divisor of the question is X

The property of the quotient is that it is a perfect square.

Thereby, let start by taking out the prime factorization of 16384 which is  

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

Now as we can see that there are four ${2}^{3}$ which if multiplied will give a perfect cube but the number multiplied by those four ${2}^{3}$ is 4. 4 is the only number which is not a cube there by if we take out 4 from the factorization then the product of ${2}^{3}$ will be perfect cube. Hence if 16384 is divided by 4, then the quotient remaining is ${({2}^{3})}^{4}$

Therefore, the smallest number that can be divided to 16384 to give the quotient a perfect cube is 4.