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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticHardLevel 4
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If (n=2^3\times3^2\times5\times7), by which number must (n) be divisible?

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Answer and explanation

Correct answer: 315

Step 1: The prime factorisation of 315 is (3^2\times5\times7). Step 2: All these factors are present in the prime factorisation of (n). Step 3: Therefore, (n) must be divisible by 315.

Related tags

DivisibilityPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

315

Why is this the correct answer?

Step 1: The prime factorisation of 315 is (3^2\times5\times7). Step 2: All these factors are present in the prime factorisation of (n). Step 3: Therefore, (n) must be divisible by 315.

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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  10. 10What is the prime factorisation of 90?
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