Question

Find the value of the smallest positive integer ‘n’ for which 864 × n is a perfect cube.

Answer 1

Answer:

2

Step-by-step explanation:

Prime factorisation of 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

They can be grouped as follows -

(2 × 2 × 2) (3 × 3 × 3)  2 × 2     [The third group has 2 missing for its triplet]

Therefore, 2 is the smallest integer to be multiplied.

Answer 2

To find : The smallest positive integer n for which 864*n is a perfect cube ?

Solution :

First we factor the number 864,

2 | 864

2 | 432

2 | 216

2 | 108

2 | 54

3 | 27

3 | 9

3 | 3

| 1

$864 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$

$864 = {2}^{3} \times 2 \times 2 \times 3 {}^{3}$

$864 = 6 {}^{3} \times 2 \times 2$

To make it a perfect cube we have to multiply 864 by 2.

i.e.

$864 \times 2 = 6 {}^{3} \times 2 \times 2 \times 2$

$1728 = 6 {}^{3} \times 2 {}^{3}$

$1728 = 12 {}^{3}$

So, the value of n is 2.

#Learn more

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