Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1+5 are composite numbers.

Question – Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1+5 are composite numbers.

Solution:

There are two types of numbers – Prime numbers and Composite Numbers.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and the number itself.

Composite numbers are numbers divisible by one or more numbers other than 1 and itself.

On simplifying 7 × 11 × 13 + 13, we get

7 × 11 × 13 + 13 = 13 ( 7 × 11 + 1 )

= 13 × ( 77 + 1 )

= 13 × 78

= 13 × 13 × 6

Hence, the given expression is divisible by 13 and 6

Therefore, 7 × 11 × 13 + 13 is a composite number.

Similarly, on simplifying 7 × 6 × 5 × 4 × 3 × 2 × 1+5

7 × 6 × 5 × 4 × 3 × 2 × 1+5 = 5 ( 7 × 6 × 4 × 3 × 2 + 1)

= 5 × (1008 + 1 )

= 5 × 1009

Hence, the given expression is divisible by 5 and 1009.

Therefore, 7 × 6 × 5 × 4 × 3 × 2 × 1+5 is a composite number.

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