Question

Find the smallest number by which 3087 must be divided so that the quotient is a perfect cube?

Answer 1

Given:

The given number = 3087

To find:

The smallest number by which 3087 must be divided so that the quotient is a perfect cube

Solution:

In order to find the required smallest no. by which 3087 must be divided, we will solve the given question in following steps:

(1). First we will find the prime factors of the number 3087.

3  | 3087

    -----------

3 |   1029

     ------------

7  |   343

     ------------

7  |     49

    -------------

         7

3087 = 3 × 3 × 7 × 7 × 7

(2). Now to make the number a perfect cube we will find the common triplets from the prime factors so received of the number 3087

Here we get,

Triplet: 7 × 7 × 7

Non-triplet: 3 × 3 

∴ We will have to divide 3087 with = 3 × 3 = 9

Thus, the required smallest no. is 9 by which 3087 must be divided so that the quotient is a perfect cube.

Verify:

$\frac{3087}{9}$ = 343 = 7³ ← perfect cube of 7

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Answer 2

Answer:

Given:

The given number = 3087

To find:

The smallest number by which 3087 must be divided so that the quotient is a perfect cube

Solution:

In order to find the required smallest no. by which 3087 must be divided, we will solve the given question in following steps:

(1). First we will find the prime factors of the number 3087.

3  | 3087

   -----------

3 |   1029

    ------------

7  |   343

    ------------

7  |     49

   -------------

        7

3087 = 3 × 3 × 7 × 7 × 7

(2). Now to make the number a perfect cube we will find the common triplets from the prime factors so received of the number 3087

Here we get,

Triplet: 7 × 7 × 7

Non-triplet: 3 × 3  

∴ We will have to divide 3087 with = 3 × 3 = 9

Thus, the required smallest no. is 9 by which 3087 must be divided so that the quotient is a perfect cube.

Verify:

= 343 = 7³ ← perfect cube of 7

-------------------------------------------------------------------------------------------------

Also View:

Find the smallest number by which 200 should be multiplied to make it a perfect cube​

brainly.in/question/14849810

Find the smallest no by which 10985 must be divided to get a perfect cube

brainly.in/question/10090370