Numbers are categorized as prime or composite. Prime numbers are divisible only by 1 and themselves. Composite numbers have factors other than 1 and themselves.
Consider the expression:
\(7 × 11 × 13 + 13 = 13 × (7 × 11 + 1)\)
\(= 13 × (77 + 1) = 13 × 78\)
\(= 13 ×13 × 6\)
This expression has 6 and 13 as factors, thus it is a composite number.
Consider the expression:
\(7 × 6 × 5 × 4 × 3 × 2 × 1 + 5\)
\(= 5 ×(7 × 6 × 4 × 3 × 2 × 1 + 1)\)
\(= 5 × (1008 + 1)\)
\(= 5 ×1009\)
As 1009 cannot be factored further, the expression has 5 and 1009 as factors. Therefore, it is a composite number.