Find the smallest number by which the number 1296 must be divided to o

1.	Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.
Answer» align="absmiddle" alt="\UNDERLINE{ \underline{ \Large \pmb{\mathit{ {Required \: Solution:}} }} }" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cunderline%7B%20%5Cunderline%7B%20%20%5CLarge%20%5Cpmb%7B%5Cmathit%7B%20%7BRequired%20%5C%3A%20Solution%3A%7D%7D%20%7D%7D%20%7D%20" title="\underline{ \underline{ \Large \pmb{\mathit{ {Required \: Solution:}} }} }"> In order to find the smallest number by which the number 1296 must be divided to obtain a perfect cube, we'll FIRST find the prime factors of the given number by prime factorization. $\large \begin{array}{c\| c} \underline{\sf{2}}& \underline{ \sf{1296}} \\ \underline{\sf{2}}& \underline{ \sf{ \: 648 \: }} \\ \underline{\sf{2}}& \underline{ \sf{ \: 324 \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: 162 \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: 54 \: \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: 18 \: \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: \: 6 \: \: \: }} \\ \underline{\sf{2}}& \underline{ \sf{ \: \: \: 2 \: \: \: }} \\ \: & \sf1\end{array}$ By prime factorization, we get : $\longrightarrow$ 1296 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 2 $\longrightarrow$ 2 × 2 × 2 × 3 × 3 × 3 × 6 So, 6 is the smallest number by which the number 1296 must be divided to obtain a perfect cube. ⠀⠀⠀⠀⠀_____________ Procedure to solve this type of questions: • Find the prime factors. • Form groups of three like factors. • The number which can't be FORMED as a group of three like factors is the number which must be divided to obtain a perfect cube.

Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.

Answer»

align="absmiddle" alt="\UNDERLINE{ \underline{ \Large \pmb{\mathit{ {Required \: Solution:}} }} }" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cunderline%7B%20%5Cunderline%7B%20%20%5CLarge%20%5Cpmb%7B%5Cmathit%7B%20%7BRequired%20%5C%3A%20Solution%3A%7D%7D%20%7D%7D%20%7D%20" title="\underline{ \underline{ \Large \pmb{\mathit{ {Required \: Solution:}} }} }">

In order to find the smallest number by which the number 1296 must be divided to obtain a perfect cube, we'll FIRST find the prime factors of the given number by prime factorization.

$\large \begin{array}{c| c} \underline{\sf{2}}& \underline{ \sf{1296}} \\ \underline{\sf{2}}& \underline{ \sf{ \: 648 \: }} \\ \underline{\sf{2}}& \underline{ \sf{ \: 324 \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: 162 \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: 54 \: \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: 18 \: \: }} \\ \underline{\sf{3}}& \underline{ \sf{ \: \: \: 6 \: \: \: }} \\ \underline{\sf{2}}& \underline{ \sf{ \: \: \: 2 \: \: \: }} \\ \: & \sf1\end{array}$

By prime factorization, we get :

$\longrightarrow$ 1296 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 2

$\longrightarrow$ 2 × 2 × 2 × 3 × 3 × 3 × 6

So, 6 is the smallest number by which the number 1296 must be divided to obtain a perfect cube.

⠀⠀⠀⠀⠀_____________

Procedure to solve this type of questions:

• Find the prime factors.

• Form groups of three like factors.

• The number which can't be FORMED as a group of three like factors is the number which must be divided to obtain a perfect cube.