Question

By what number should 40500 be divided to obtain perfect cube

Answer 1

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Answer 2

The number that should be divide 40500 to obtain perfect cube is 12

Given:

Number 40500  

To find:

By what number should 40500 be divided to obtain perfect cube

Solution:

Perfect cube number

• Perfect cube number is a positive number which is obtained by multiplying a number 3 times
• Example:

        8 is a perfect cube since 2×2×2 = 8 = 2³

        27 is a perfect cube since 3×3×3 = 27 = 3³

        15625 is perfect cube since 25×25×25 = 15625 = 25³

• From above examples we can say that a perfect cube number can be write in a³ form.          

Given number 40500  

Write given number as product of its prime factors

40500 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5    

Now group the given numbers as triples

= 3³× 5³ × 2 × 2 × 3

After grouping the factors we can see that 2 × 2 × 3 are left out

So, to get a perfect cube from 40500 we need reduce 2 × 2 × 3

Here, 2 × 2 × 3 = 12

Therefore,

The number that should be divide 40500 to obtain perfect cube is 12

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