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Find the HCF of the… (Class 10 Maths Basic 2023, Q22a)

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

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

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

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

Find the HCF of the numbers 540 and 630, using prime factorization method.

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

Break each number into a product of primes by repeated division.

Hint 2

For the HCF, take only the primes common to both numbers, each with its smaller power.

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. ½ mark

  2. ½ mark

  3. HCF is the product of the smallest powers of the common prime factors:

    1 mark

Answer: HCF(540, 630) = 90

Where the marks are

  • Correct prime factorisation of 540 (1/2 mark)
  • Correct prime factorisation of 630 (1/2 mark)
  • HCF (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.