Question

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

Answer 1

Composite Number :  

A number is called a composite number if it has at least one factor other than one and the number itself.

Composite number = product of prime numbers.

Or

Any Integer greater than 1, either be a prime number or can be written as a product of prime factors.

SOLUTION:

Given : 7 x 11 x 13 + 13

7 x 11 x 13 + 13 = (1001 +13) = 1014

1014 = 2 × 3 × 13 × 13

Here, 1014 is the product of more than two prime numbers i.e  2,3 and 13.

So, it is a composite number.

Given : 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5

7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = (5040 + 5 ) = 5045

5045 = 5 × 1009

Thus , it is the product of prime factors 5 and 1009.  

Hence, it is also a composite Number.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:A number is called a composite number if it has at least one factor other than one and the number itself.

Composite number = product of prime numbers.

Or

Any Integer greater than 1, either be a prime number or can be written as a product of prime factors.

SOLUTION:

Given : 7 x 11 x 13 + 13

7 x 11 x 13 + 13 = (1001 +13) = 1014

1014 = 2 × 3 × 13 × 13

Here, 1014 is the product of more than two prime numbers i.e  2,3 and 13.

So, it is a composite number.

Given : 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5

7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = (5040 + 5 ) = 5045

5045 = 5 × 1009

Thus , it is the product of prime factors 5 and 1009.  

Hence, it is also a composite Number.