Question

4. What is the smallest number by which the following numbers must be
the products are perfect cubes?
(i) 107811 ​

Answer 1

Given:

$\sf\ Product=107811$

To find:

$\sf\ Smallest\: number\:of\:107811$

Required Solution:

$\sf\ First\:find\: factors\:of\:107811.$

$\dashrightarrow\: \sf\ 107811=3×3×3×3×11×11×11$

$\dashrightarrow\: \sf\ 3^3×3×11^3$

$\sf\ To\:make\:a\: perfect\:cube\:we\:need$

$\sf\ to\:multiply\:the\: products$

$\dashrightarrow\: \underline{\boxed{\bf{\red{3×3=9}}}}.$

Answer 2

Answer:

Step-by-step explanation:

107811 : Sum of digits is nine , so it is divisible by 9 and also by 11 since difference of sum of alternate digits is 0.

$107811 = 9^2 * 11^3$

$107811 = 3^4 * 11^3$

Hence it should be multiplied by 9 to make it a perfect cube.(970299)

It should be divided by 3 to make it a perfect cube.(35937)