MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerReal Numbers

Using prime factorisation, find the HCF of 180, 140 and 210.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Break each number into primes by repeated division.

Hint 2

Pick only the primes common to all three, each with its lowest 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.

Prime factorisations:
$180 = 2^{2} \times 3^{2} \times 5$
$140 = 2^{2} \times 5 \times 7$
$210 = 2 \times 3 \times 5 \times 7$
1½ marks
HCF = product of the smallest powers of the common prime factors $= 2^{1} \times 5^{1} = 10$ .
½ mark

Answer: HCF = 10

Where the marks are

Correct prime factorisation of 180, 140 and 210 (1½ marks)
HCF $= 2 \times 5 = 10$ (½ mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: HCF and LCM by Prime Factorisation

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 25

Hints

Step-by-step solution

Revise the chapter

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