Question

find the least number that should be divided so that 1280 will be a perfect cube.
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Answer 1

Answer:

The number that should be divided to 1280 to make it a perfect cube is 20.

Step-by-step explanation:

Perfect cube:

• Numbers that are the triple product of the same number are known as perfect cubes. In other words, the value produced by multiplying a whole number by three times itself is a perfect cube.
• A number that may be expressed as three times the product of another integer is referred to as a perfect cube.

The given number is 1280.

The least by which 1280 is divided to get a perfect cube is 2.

 By Prime factorization we can write

      1280 = 2×2×2×2×2×2×2×2×5

    When we divide 1280 with 20 then we get 64

      64 is a perfect cube of 4.

    So, the number that should be divided to 1280 is 20.

Know more about Division:

https://brainly.in/question/13368512?referrer=searchResults

Know more about Perfect square:

https://brainly.in/question/43418979?referrer=searchResults

Answer 2

Answer:

The required number is 20.

Step-by-step explanation:

To find:-

The least number that should be divided from 1280 to make it a perfect cube.

Consider the given number as follows:

1280

Compute the cube root of the number 1280 as follows:

$\sqrt[3]{1280}=\sqrt[3]{2\times2\times2\times2\times2\times2\times2\times2\times5}$

          $=\sqrt[3]{2^6\times2\times2\times5}$

          $=4\sqrt[3]{20}$

Notice that the number 20 cannot be written as the perfect cube.

So,

Divide the given number 1280 by 20 as follows:

⇒ 1280/20

⇒ 64

Observe that the number 64 is the perfect cube of the number 4, i.e.,

$4^3$ = 4 × 4 × 4

   = 64

Therefore, 20 is the least number that should be divided so that 1280 will be a perfect cube.

Final answer: The required number is 20.

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