CBSE Class 10 Mathematics Standard 2024: question 21

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Step-by-step solution

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1. Prime factorisation: $15^n=(3\times 5{)}^n=3^n\times 5^n$.

   1 mark

2. A number ends with the digit $0$ only if it is divisible by $10=2\times 5$, so its prime factorisation must contain both $2$ and $5$. By the uniqueness of prime factorisation (Fundamental Theorem of Arithmetic), $15^n$ has only the primes $3$ and $5$, with no $2$. Hence $15^n$ can never end with the digit $0$ for any natural number $n$.

   1 mark

Answer: No; $15^n=3^n\cdot 5^n$ has no prime factor 2, so it cannot end with 0.

Revise the chapter

• Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
• Topic: Fundamental Theorem of Arithmetic