How will you show that $(17 \times 11 \times 2) + (17 \times 11 \times 5)$ is a composite number? Explain.

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Solution

Consider $(17 \times 11 \times 2) + (17 \times 11 \times 5)$

$= 17 \times 11 \times (2 + 5)$

$= 17 \times 11 \times 7$ is a composite number.

Since, according to Fundamental theorem of arithmetic, every composite number can be expressed as the product of powers of primes and their factorisation is unique, except for the order in which the prime factors occur.

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