6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution: By the definition of composite number, we know, if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression; 7 × 11 × 13 + 13 Taking 13 as common factor, we get, =13(7×11×1+1) = 13(77+1) = 13×78 = 13×3×2×13 Hence, 7 × 11 × 13 + 13 is a composite number. Now let’s take the other number, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 Taking 5 as a common factor, we get, =5(7×6×4×3×2×1+1) = 5(1008+1) = 5×1009 Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.