Question

find the smallest number which must be multiplied and divide so as the resuting number a perfect cube 23328

Answer 1

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The least number by which 23328 should be divided to make it a perfect cube

The cube root of each perfect cube

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The given number is 23328

$\sf\green{23328}$

$\sf{2 \times2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 }$

$\implies \sf{23328 = {2}^{5} \times {3}^{6} }$

$\implies \sf{23328 = {2}^{3} \times {2}^{2} \times { {(3}^{2}) }^{3} }$

$\implies \sf{23328 = {2}^{3} \times {2}^{2} \times { 9 }^{3} }$

Hence in order to make a perfect cube 23328 should be divided by 4

Then the reduced number is 5832

$\sf{5832 = {2}^{3} \times {9}^{3} \: }$

So that cube root of 5832 = 2 × 9 = 18