Skip to content

Show that (15)^n cannot… (Class 10 Maths Basic 2023, Q22b)

questionbuddy.in/q/cbse-10-maths-2023-430-2-1-q22b-cannot-end-digit-natural-number

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 22(b)

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerReal Numbers

Show that cannot end with the 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 430/2/1.

Hints

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

Hint 1

Write 15 as a product of primes and raise it to the power n.

Hint 2

A number ending in 0 must be divisible by 10. Which primes make up 10?

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. , so the only prime factors of are 3 and 5.

    1 mark

  2. A number ending in 0 is divisible by 10 , so 2 must appear in its prime factorisation. Since 2 is not a prime factor of (by uniqueness of prime factorisation, Fundamental Theorem of Arithmetic), cannot end with the digit 0 for any natural number .

    1 mark

Answer: has no factor 2, so it cannot end with 0.

Where the marks are

  • Writes (1 mark)
  • Argues that ending in 0 needs prime factors 2 and 5, and 2 is absent, so cannot end in 0 (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 430/2/1 (Basic): 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.