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Explain why $7 \times 11 \times 13 + 13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+ 5$ are composite numbers.
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$7 \times 11 \times 13 + 13 = 13 \times 78$ or $2 \times 3 \times 13^2$ (1)
and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5 = 5 \times 1009$ ($\frac{1}{2}$)
Both numbers have two factors other than $1$
$\therefore$ both the numbers are composite ($\frac{1}{2}$)
and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5 = 5 \times 1009$ ($\frac{1}{2}$)
Both numbers have two factors other than $1$
$\therefore$ both the numbers are composite ($\frac{1}{2}$)