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

7×11×13+13
Taking 13 as common,  we get,
 13×(7×11+1) = 13×(77+1)
= 13×78
= 13×13×6
The given expression has 6 and 13 as its factors.
Therefore, it is a composite number.

7×6×5×4×3×2×1+5
Taking 5 as common , we get,
= 5×(7×6×4×3×2×1+1)
= 5× (1008+1)
= 5×1009
1009 cannot be factorised further.
Therefore, the given expression has 5 and 1009 as its factors.
Hence, it is a composite number.