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.
To explain: The given numbers are composite numbers.
Let's first see the number \(7 \times 11 \times 13 + 13\).
\(=\) \(7 \times 11 \times 13 + 13\)
\(=\) \((7 \times 11 + 1)\)
\(=\) \((77 + 1)\)
\(=\) \((78)\)
\(=\) \(13 \times 2 \times 3 \times 13\)
Since it has more than two factors \((1, 2, 3, 13, 78)\),
\(7 \times 11 \times 13 + 13\) is a
Now, see the number \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5\).
\(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5\)
\(=\) \( (7 \times 6 \times 4 \times 3 \times 2 \times 1 + 1)\)
\(=\) \((1008 + 1)\)
\(=\) \((1009)\)
\(=\)
Since it has more than two factors \((1, 5, 1009)\), \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5\) is a