CBSE Class 10 Mathematics Basic 2025: question 21

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Step-by-step solution

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1. Write the number in prime factor form: $15^n\times 2^n=(3\times 5{)}^n\times 2^n=2^n\times 3^n\times 5^n$.

   1 mark

2. A number ends with the digit zero when its prime factorisation contains both 2 and 5. Here 2 and 5 are both factors for every natural number $n$, so $15^n\times 2^n$ (which equals $10^n\times 3^n$) ends with the digit zero.

   1 mark

Answer: Yes, $15^n\times 2^n=2^n\times 3^n\times 5^n$ has both 2 and 5 as factors, so it ends with the digit zero.

Revise the chapter

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