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

Dear Student

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 + 13is 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 + 5is a composite number.

​Thanks