By definition,

A composite number is a positive integer that has a factor other than 1 and itself. Now considering your numbers,

7×11×13 + 13 may be written as, i.e. 13 * (78). So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78 = 39 x 2. So, 39 and 2 are also its factors. So this number is definitely not prime. Hence its composite number.

Similarly, 7×6×5×4×3×2×1 + 5 can be written as , i.e. 5 * (1009). So, other than the number and 1, it have 5 and 1009 as its factors too. So it is also a composite number.

OR

If any number ends with the digit 0, it should be divisible by 10 or in other words its prime factorization must include primes 2 and 5 both as 10 = 2 ×5

Prime factorization of 6ⁿ = (2 ×3) ⁿ

In the above equation it is observed that 5 is not in the prime factorization of 6ⁿ

By Fundamental Theorem of Arithmetic Prime factorization of a number is unique. So, 5 is not a prime factor of 6ⁿ.

Hence, for any value of n, 6ⁿ will not be divisible by 5.

Therefore, 6ⁿ cannot end with the digit 0 for any natural number n.