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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 4
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Which is the prime factorisation of 176400?

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Answer and explanation

Correct answer: (2^4\times3^2\times5^2\times7^2)

Step 1: Recognise (176400=420^2). Step 2: Since (420=2^2\times3\times5\times7), (420^2=2^4\times3^2\times5^2\times7^2). Step 3: In a perfect square, every prime exponent is even.

Related tags

Prime-FactorisationPerfect-SquareExpert

Frequently asked questions

What is the correct answer to this question?

(2^4\times3^2\times5^2\times7^2)

Why is this the correct answer?

Step 1: Recognise (176400=420^2). Step 2: Since (420=2^2\times3\times5\times7), (420^2=2^4\times3^2\times5^2\times7^2). Step 3: In a perfect square, every prime exponent is even.

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?
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