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Show that 6^n can not end with… (Class 10 Maths 2023, Q21A)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 21(A)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 21(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(A) · 2 marks · Very short answerReal Numbers

Show that can not end with digit 0 for any natural number 'n'.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Which primes must divide a number that ends in 0?

Hint 2

Write as a product of prime powers and check whether 5 can appear.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. Any number ending in the digit 0 is divisible by both 2 and 5, so its prime factorisation must contain the prime 5.

    1 mark

  2. Here . By the Fundamental Theorem of Arithmetic this factorisation is unique, so the only primes in are 2 and 3. The prime 5 never appears. Hence cannot end with the digit 0 for any natural number .

    1 mark

Answer: has no factor 5, so it can never end in 0.

Where the marks are

  • States that ending in 0 needs 5 in the prime factorisation (1 mark)
  • Writes and uses the uniqueness of factorisation to conclude (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/6/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.