Question

Why $$5\times 6\times 7\times 11-2\times 3\times 7\times 11$$ is a composite number?

Answer 1

Hint: We have to directly find the products of the terms and then difference between them. If the difference is a composite number then the answer is yes, the given problem is a composite number.

Complete step-by-step answer:
Given that,
$$5\times 6\times 7\times 11-2\times 3\times 7\times 11$$
$$\begin{gathered} \Rightarrow 5\times 2\times 3\times 7\times 11-2\times 3\times 7\times 11 \\ \Rightarrow (2\times 3\times 7\times 11)(5-1) \\ \Rightarrow 2\times 3\times 7\times 11\times 4 \\ \Rightarrow 6\times 77\times 4 \\ \Rightarrow 24\times 77 \\ \Rightarrow 1848 \end{gathered}$$
Since this number is a composite number we can say the given difference is a composite number.
Because this number is divisible by more than two numbers.

Note: Composite numbers are the numbers having more than two factors.
Ex 12 ,2 5, 42 , 64 .
Prime numbers are the numbers having only two factors 1 and the number itself.
Ex.2, 3 ,5 ,11
Product of composite numbers is always a composite number.
Ex. $$6\times 8=48$$
Product of prime numbers is also a composite number.
Ex. $$3\times 7$$ $$=21$$
Difference of two composite numbers is always composite, but not of prime numbers necessarily.