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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 2 · Set 2 · Q23
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Explain why $\displaystyle 7$ × $\displaystyle 11$ × $\displaystyle 13$ + $\displaystyle 13$ and $\displaystyle 7$ × $\displaystyle 6$ × $\displaystyle 5$ × $\displaystyle 4$ × $\displaystyle 3$ × $\displaystyle 2$ × $\displaystyle 1$ + $\displaystyle 5$ are composite numbers.
Marking-scheme solution
\[\begin{aligned}
& 7 \times 11 \times 13+13=13 \times 78 \text { or } 2 \times 3 \times 13^{2} \\
& \text { and } 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1+5=5 \times 1009
\end{aligned}
\]
Both numbers have two factors other than $\displaystyle 1$
∴ both the numbers are composite
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