Show that the number $5 \times 11 \times 17 + 3 \times 11$ is a composite number.
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
$5 \times 11 \times 17 + 3 \times 11$
$= 11(5 \times 17 + 3)$
$= 11(85 + 3)$
$= 11 \times 88$
$= 11 \times 8 \times 11$
$= 8 \times 11^2$
Since the number can be expressed as a product of factors (other than 1 and itself), it is a composite number.
Source: Chapter 1, The Fundamental Theorem of Arithmetic
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Explanation
- The key step is taking 11 as a common factor. This immediately shows the number is divisible by 11 (and also by 8), so it has factors other than 1 and itself — the definition of a composite number.
- Examiners expect you to show the factorisation step-by-step and explicitly state the conclusion. Do not just calculate the final value (968); show why it is composite by exhibiting its factors.
- This is similar to Exercise 1.1, Q.6 from Chapter 1.