5(7×6×4×3×2×1)+1
=5(1008)+1
=5×1009
=5045
we know every composite have at least 3 factors
Here 5045 was written as product of two prime numbers 5 and 1009
Here 5045 is also the factor of itself and 1is also the factor of 5045
Then 5045 has four factors
Therefore (7×6×5×4×3×2×1)+5 is a composite number

Is 7×6×5×4×3×2×1 5 a composite number?

To determine whether the number 7×6×5×4×3×2×1 + 5 is a composite number, we need to understand the definition of a composite number and how it applies to the given expression.

Definition of a composite number:
A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. In other words, composite numbers can be divided evenly by numbers other than 1 and themselves.

Step 1: Calculate the value of 7×6×5×4×3×2×1 + 5:
Let's calculate the value of the expression 7×6×5×4×3×2×1 + 5:
7×6×5×4×3×2×1 + 5 = 5040 + 5 = 5045

Step 2: Determining if 5045 is a composite number:
To determine if 5045 is a composite number, we need to check if it has any divisors other than 1 and itself. We can do this by performing a prime factorization of 5045.

Prime factorization of 5045:
To find the prime factorization of 5045, we can start by dividing it by the smallest prime number, which is 2. However, 5045 is an odd number, so it cannot be divisible by 2. We can then try dividing it by the next prime number, which is 3.

5045 ÷ 3 = 1681
1681 ÷ 3 = 560.33 (not divisible by 3)
560.33 ÷ 3 = 186.77 (not divisible by 3)

Since 560.33 and 186.77 are not whole numbers, we can conclude that 5045 is not divisible by 3.

Step 3: Checking for other divisors:
We can continue checking for other prime numbers as potential divisors. By doing so, we find that 5045 is not divisible evenly by any prime numbers up to its square root, which is approximately 71. Therefore, we can conclude that 5045 does not have any divisors other than 1 and itself.

Conclusion:
Since 5045 does not have any other divisors besides 1 and itself, it does not meet the definition of a composite number. Therefore, the expression 7×6×5×4×3×2×1 + 5 is not a composite number.