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Subjects
Class 10MathematicsReal NumbersPrime FactorisationHardLevel 9

If the number is (2^{10}\times3^8\times5^5\times7^4), by which smallest number should it be divided to make a perfect cube?

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Answer and explanation

Correct answer: (2\times3^2\times5^2\times7)

Step 1: For a perfect cube, exponents should be multiples of 3. Step 2: Reducing 10 to 9, 8 to 6, 5 to 3, and 4 to 3 is the smallest way. Step 3: Therefore, the divisor is (2\times3^2\times5^2\times7).

Tags

perfect-cubedivisionhard

Frequently asked questions

What is the correct answer to this question?

(2\times3^2\times5^2\times7)

Why is this the correct answer?

Step 1: For a perfect cube, exponents should be multiples of 3. Step 2: Reducing 10 to 9, 8 to 6, 5 to 3, and 4 to 3 is the smallest way. Step 3: Therefore, the divisor is (2\times3^2\times5^2\times7).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.

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