Answer: The answer is that 7×11×13+7 simplifies to 1008, which is a composite number. Therefore, 7×11×13+7 is a composite number.
Step-by-step explanation: To determine whether the expression 7×11×13+7 is a composite number or not, we first need to simplify the expression using the order of operations (PEMDAS):
7×11×13+7 = 1001 + 7
= 1008
Now, to determine whether 1008 is a composite number, we need to check if it has any factors other than 1 and itself.
One way to do this is to check if 1008 is divisible by any prime numbers less than or equal to its square root (because any composite number can be factored into prime factors, and at least one of those factors must be less than or equal to the square root of the number).
The square root of 1008 is approximately 31.75, so we only need to check for divisibility by the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 (all of which are less than or equal to 31.75).
We can check that 1008 is divisible by 2 (because its last digit is even) and by 3 (because the sum of its digits is divisible by 3), but it is not divisible by any of the other primes.
Therefore, we can conclude that 1008 is a composite number (because it has factors other than 1 and itself), and hence, the expression 7×11×13+7 is also a composite number.