Assertion (A): H.C.F. (36m², 18m) = 18m, where m is a prime number. Reason (R): H.C.F. of two numbers is always less than or equal to the smaller number. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2026: question 20

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedReal Numbers

Assertion (A): H.C.F. $(36 m^{2}, 18 m) = 18 m$ , where $m$ is a prime number.

Reason (R): H.C.F. of two numbers is always less than or equal to the smaller number.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Factorise both expressions into primes.

Hint 2

Does R actually explain why the HCF equals 18m?

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.

$36 m^{2} = 2^{2} \cdot 3^{2} \cdot m^{2}$ , $18 m = 2 \cdot 3^{2} \cdot m$ ; HCF $= 2 \cdot 3^{2} \cdot m = 18 m$ . A is true.
R is true (HCF divides both numbers, so it cannot exceed the smaller), but A is established by prime factorisation, not by R. Option (B).
1 mark

Answer: Option (B)

Where the marks are

Verifies HCF = 18m and recognises R is true but not the explanation (1 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 paper2026 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 20

Hints

Step-by-step solution

Revise the chapter

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