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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 4
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If (n=2^8\times3^4\times5^2), by which of the following will (n) not be divisible?

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Answer and explanation

Correct answer: 3375

Step 1: In (n), the powers are (2^8), (3^4), and (5^2). Step 2: (3375=3^3\times5^3), which needs power 3 of 5. Step 3: Since (n) has only (5^2), (n) is not divisible by 3375.

Related tags

DivisibilityPrime-FactorisationExpert

Frequently asked questions

What is the correct answer to this question?

3375

Why is this the correct answer?

Step 1: In (n), the powers are (2^8), (3^4), and (5^2). Step 2: (3375=3^3\times5^3), which needs power 3 of 5. Step 3: Since (n) has only (5^2), (n) is not divisible by 3375.

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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  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?
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  8. 8Which of the following numbers is prime?
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