Show that the number 5×11×17+3×11 is a composite number.

5×11×17+3×11 = 11×88 = 2³×11², so it is composite.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 25(B)

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section B, question 25(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(B) · 2 marks · Very short answerReal Numbers

Show that the number $5 \times 11 \times 17 + 3 \times 11$ is a composite number.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Is there a factor common to both terms?

Hint 2

After taking out the common factor, can the number be prime?

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 out as a common factor: $5 \times 11 \times 17 + 3 \times 11 = 11 \times (5 \times 17 + 3)$ .
1 mark
Simplify the bracket: $= 11 \times (85 + 3) = 11 \times 88 = 11 \times 11 \times 2^{3}$ $(= 968)$ .
½ mark
The number has factors other than 1 and itself (for example 11 and 88). Hence it is a composite number.
½ mark

Answer: $5 \times 11 \times 17 + 3 \times 11 = 11 \times 88 = 2^{3} \times 1 1^{2}$ , so it is composite.

Where the marks are

Takes 11 out as a common factor (1 mark)
Simplifies to $11 \times 88$ or $2^{3} \times 1 1^{2}$ (½ mark)
Concludes the number is composite because it has factors other than 1 and itself (½ 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 paper2024 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 25(B)

Hints

Step-by-step solution

Revise the chapter

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