Question

What is the smallest number by which 82944 should
be divided so that the quotient is a perfect cube?

Answer 1

Answer:

13

Step-by-step explanation:

The given number is 8788

The prime factorisation of 8788 is given by,

8788=2×2×13×13×13

We see that prime factor 2 does not occur in the group of 3, hence the given number is not a perfect cube.

In order to make it a perfect cube, it must be divided by 4.

Now,  

8788​/4

=  

2×2×13×13×13

__________

         4

⇒2197=13×13×13, which is a perfect cube number.

Thus, the cube root of 2197=13

Answer 2

The smallest number which will divided 8640 in order get a perfect cube is 6

Given:

82944

To find:

The smallest number by which 82944 should be divided so that the quotient is a perfect cube

Solution:

[Note: A perfect cube is a multiple of a triplet of digits.]  

To find the smallest number which will divided 8640, write it as product of its prime factors

82944 = 2¹⁰ x 3⁴

Now group the above factor as triplet

2¹⁰ x 3⁴ = 2³ × 2³ × 2³ × 2 × 3³ × 3  

After grouping factor as triplet the left out digits are 2 × 3

⇒ 2 × 3 = 6

Therefore, the smallest number which will divided 8640 in order get perfect cube is 6

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