Question

divide the number 26244 by the smallest number so that quotient obtained is a perfect cube. also find the cube root of a perfect cube obtained​

Answer 1

prime factorisation of 26244

26244 = 2×2×3×3×3×3×3×3×3×3

Now,

make triplets of three factors.

So, we get the 2 triplets of 3.

Now, multiply the rest of the factors that is

2×2×3×3 = 36

Now,

divide 26244 by 36 to get a perfect cube.

26244 ÷ 36 = 729

Now,

cube root of 729 is 9.

Answer 2

Given : divide the number 26244 by the smallest number so that quotient obtained is a perfect cube.

To Find : smallest number

the cube root of a perfect cube obtained​

Solution:

                26244

    2          13122

    2           6561

   3            2187

   3             729

   3             243

   3                81

   3                27

   3                9

   3                3

    3                1

               

26244   = 2 * 2 * 3 * 3 *  3 * 3 * 3 * 3 * 3 * 3

= 2 * 2 * 3³  * 3³  * 3 * 3

= 4 *  (3 * 3)³ * 9

= 36 * 9³

smallest number is 36  by which number 26244 should be divided to get perfect cube

and obtained perfect cube  is  9³

Hence cube root of  perfect cube obtained​  is 9

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