The HCF of 40, 110 and 360 is : (A) 40 (B) 110 (C) 360 (D) 10

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 18

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q18 · 1 mark · MCQReal Numbers

The HCF of $40$ , $110$ and $360$ is :

(A) $40$
(B) $110$
(C) $360$
(D) $10$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Write each number as a product of primes.

Hint 2

The HCF is the product of the smallest powers of the common primes.

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.

$40 = 2^{3} \times 5$ , $110 = 2 \times 5 \times 11$ , $360 = 2^{3} \times 3^{2} \times 5$ .
½ mark
Common primes with their lowest powers: $2 \times 5 = 10$ . So HCF $= 10$ . Option (D).
½ mark

Answer: 10, option (D)

Where the marks are

Prime factorises all three numbers and takes the lowest common powers to get 10, option (D) (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 paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 18

Hints

Step-by-step solution

Revise the chapter

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