question_answer

Explain why \[(17\times 5\times 11\times 3\times 2+2\times 11)\] is a composite number?

Answer:

\[17\times 5\times 11\times 3\times 2+2\times 11=17\times 5\times 3\times 22+22\]                          ...(i)

\[=22\,(17\times 5\times 3+1)\]

\[=22\text{ (}255+1)=2\times 11\times 256\]

Equation (i) is divisible by 2, 11 and 256, which means it has more than 2 prime factors.

\[\therefore \,\,(17\times 5\times 11\times 3\times 2+2\times 11)\] is a composite number.