Show that the number 2 × 5 × 7 × 11 + 11 × 13 is a composite number.

2×5×7×11+11×13 = 11×83, so it is composite.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 21(A)

From the official CBSE sample question paper for 2025-26, section B, question 21(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(A) · 2 marks · Very short answerReal Numbers

Show that the number $2 \times 5 \times 7 \times 11 + 11 \times 13$ is a composite number.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Look for a factor that appears in both terms.

Hint 2

Take 11 common and simplify what is left in the bracket.

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.

Take 11 common: $2 \times 5 \times 7 \times 11 + 11 \times 13 = 11 \times (2 \times 5 \times 7 + 13) = 11 \times (70 + 13) = 11 \times 83$
1 mark
The number equals $11 \times 83 = 913$ . It has factors 11 and 83 besides 1 and itself, so it is a composite number.
1 mark

Answer: $2 \times 5 \times 7 \times 11 + 11 \times 13 = 11 \times 83$ , so it is composite.

Where the marks are

Takes 11 common and writes the number as $11 \times 83$ (1 mark)
Concludes it is composite because it has factors other than 1 and itself (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 21(A)

Hints

Step-by-step solution

Revise the chapter

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