Numbers are of two types - prime and composite.
Prime numbers has only two factors namely 1 and the number itself whereas composite numbers have factors other than 1 and itself.
For example:
7 is a prime number as it can be divided by 1 and 7 only whereas 14 is a composite number as it can be divided by 7, 2 and 1
From the question it can be observed that,
7 × 11 × 13 + 13 = 13 × (7 × 11 + 1) = 13 × (77 + 1) [ taking 13 common ]
= 13 × 78
= 13 × 13 × 6
The given expression has 6 and 13 as its factors.
Therefore, it is a composite number.
7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 × (7 × 6 × 4 × 3 × 2 x 1 + 1)
= 5 × (1008 + 1)
= 5 ×1009
In the above we observe that 1009 cannot be factorized further.
Therefore, the given expression has 5 and 1009 as its factors.
Hence, it is a composite number.
