Question

The smallest positive integer n for which 864*n is a perfect cube is

Answer 1

Answer:

Step-by-step explanation:

According to the question,

2 | 864

2 | 432  

6 | 216

6 | 36

6 | 6

| 1  

2×2×n×6×6×6

Here n = 2

Answer 2

The value of n is 2.

Step-by-step explanation:

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.

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