Q - find a smallest number by which 5400 be multiple to make it a perfect cube
Answers
Step-by-step explanation:
First we find the factors of 5400 by division method
\begin{gathered}\begin{array}{r|l}2&5400\\\cline{2-2}2&2700\\\cline{2-2}2&1350\\\cline{2-2}5&675\\\cline{2-2}5&135\\\cline{2-2}3&27\\\cline{2-2}3&9\\\cline{2-2}3&3\\\cline{2-2}&1\\\cline{2-2}\end{array}\end{gathered}
2
\cline2−22
\cline2−22
\cline2−25
\cline2−25
\cline2−23
\cline2−23
\cline2−23
\cline2−2
\cline2−2
5400
2700
1350
675
135
27
9
3
1
5400=2{\times}2{\times}2{\times}5{\times}5{\times}3{\times}3{\times}35400=2×2×2×5×5×3×3×3
\implies\,5400=2^3{\times}3^3{\times}5^2⟹5400=2
3
×3
3
×5
2
\text{Here, 5 occurs only two times}Here, 5 occurs only two times
\text{When 5 is multiplied to 5400, it will become a perfect cube}When 5 is multiplied to 5400, it will become a perfect cube
27000=2^3{\times}3^3{\times}5^327000=2
3
×3
3
×5
3
\text{Now,the factorization of 27000 contains product of cubes of all its factors}Now,the factorization of 27000 contains product of cubes of all its factors
\therefore\textbf{The required smallest number is 5}∴The required smallest number is 5
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