Question

What is the smallest number should 7803be multiplied with so that the product become perfect cube

Answer 1

7803=3 X 3 X 3 X 17 X 17

ANS= 17"AS IT SHOULD BE MULTIPLIED"

Answer 2

Hi there!
Here's the answer:

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Type of problem :
To find the smallest number that should be multiplied by number 'x' so that resultant product becomes a perfect cube

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Approach to problem
Steps:

•Resolve the number into prime factors
• Express the number as product of prime factors in exponential form
• The Prime factor that are not having 3 as their power should be multiplied to the number x so that the product is a perfect cube.


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Now,
Given Number = 7803

…3 | 7803
…3 | 2601
…3 | 867
..17 | 279
……| 17


7803 = 3 × 3 × 3 × 17 × 17

In Exponential form,
7803 = 3³ × 17²

Here 17 is the number that is not having 3 as its power.
•°• The Number 17 is to be multiplied with 7803 to make it a perfect cube.

•°• Required least Number = 17.


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:)


Hope it helps