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Find the greatest number which… (Class 10 Maths 2023, Q24)

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

CBSE Class 10 Mathematics Standard 2023: question 24

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerReal Numbers

Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.

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

Hints

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

Hint 1

If a number leaves remainder 1 on dividing 85, what does it divide exactly?

Hint 2

Subtract each remainder from its number, then find the greatest common divisor of the two results.

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. The required number leaves remainder 1 when it divides 85, so it divides exactly. It leaves remainder 2 when it divides 72, so it divides exactly. Hence the required number is the HCF of 84 and 70.

    1 mark

  2. Write the prime factorisations: and .

    So HCF .

    The greatest such number is 14.

    1 mark

Answer: 14

Where the marks are

  • Reduces the problem to the HCF of 84 and 70 (1 mark)
  • Finds HCF = 14 (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 30/1/1 (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.