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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 4
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If (p=2^a\times3^4\times5\times7) and (p=45360), what is the value of (a)?

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Answer and explanation

Correct answer: 4

Step 1: Write (45360=648\times70). Step 2: (648=2^3\times3^4) and (70=2\times5\times7), so (45360=2^4\times3^4\times5\times7). Step 3: Comparing gives (a=4).

Related tags

Exponent-ComparisonPrime-FactorisationExpert

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

Step 1: Write (45360=648\times70). Step 2: (648=2^3\times3^4) and (70=2\times5\times7), so (45360=2^4\times3^4\times5\times7). Step 3: Comparing gives (a=4).

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?
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  6. 6The number (2^3\times3^2) is equal to which number?
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