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,
\[5 \times 6 \times 7 \times 11 - 2 \times 3 \times 7 \times 11\]
\[
   \Rightarrow 5 \times 2 \times 3 \times 7 \times 11 - 2 \times 3 \times 7 \times 11 \\
   \Rightarrow (2 \times 3 \times 7 \times 11)(5 - 1) \\
   \Rightarrow 2 \times 3 \times 7 \times 11 \times 4 \\
   \Rightarrow 6 \times 77 \times 4 \\
   \Rightarrow 24 \times 77 \\
   \Rightarrow 1848 \\
\]
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.