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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 4
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What is the smallest number by which 15120 must be multiplied to get a perfect cube?

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Answer and explanation

Correct answer: 2450

Step 1: (15120=2^4\times3^3\times5\times7). Step 2: For a perfect cube, exponents must be multiples of 3. Step 3: Multiplying by (2^2\times5^2\times7^2=2450) makes the powers 6, 3, 3, and 3.

Related tags

Perfect-CubePrime-FactorisationExpert

Frequently asked questions

What is the correct answer to this question?

2450

Why is this the correct answer?

Step 1: (15120=2^4\times3^3\times5\times7). Step 2: For a perfect cube, exponents must be multiples of 3. Step 3: Multiplying by (2^2\times5^2\times7^2=2450) makes the powers 6, 3, 3, and 3.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Fundamental Theorem of Arithmetic.

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  1. 1According to the Fundamental Theorem of Arithmetic, every composite number can be written in which form?
  2. 2What is the prime factorisation of 36?
  3. 3What is the correct prime factorisation of 60?
  4. 4What does uniqueness mean in the Fundamental Theorem of Arithmetic?
  5. 5In the prime factorisation of 84, what is the power of 2?
  6. 6The number (2^3\times3^2) is equal to which number?
  7. 7Which is the prime factorisation of 45?
  8. 8Which of the following numbers is prime?
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