Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are com

1.	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» So, basically there are two types of numbers i.e., prime numbers and composite numbers. Understanding that, Prime numbers are those numbers having 1 and the number itself as factors. And, Composite numbers are those numbers having factors other than 1 and itself. It’s seen that, 7 x 11 x 13 + 13 = 13 x (7 x 11 + 1) [taking 13 out as common] = 13 x (77 + 1) = 13 x 78 = 13 x 13 x 6 So, the given expression has 6 and 13 as its factors. Therefore, we can conclude that it is a composite number. Similarly, 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 5 x (7 x 6 x 4 x 3 x 2 x 1 + 1) [taking 5 out- common] = 5 x (1008 + 1) = 5 x 1009 Since, 1009 is a prime number the given expression has 5 and 1009 as its factors other than 1 and the number itself. Hence, it is also a composite number.

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»

So, basically there are two types of numbers i.e., prime numbers and composite numbers.

Understanding that,

Prime numbers are those numbers having 1 and the number itself as factors. And,

Composite numbers are those numbers having factors other than 1 and itself.

It’s seen that,

7 x 11 x 13 + 13 = 13 x (7 x 11 + 1) [taking 13 out as common]

= 13 x (77 + 1)

= 13 x 78

= 13 x 13 x 6

So, the given expression has 6 and 13 as its factors. Therefore, we can conclude that it is a composite number.

Similarly,

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

= 5 x (7 x 6 x 4 x 3 x 2 x 1 + 1) [taking 5 out- common]

= 5 x (1008 + 1)

= 5 x 1009

Since, 1009 is a prime number the given expression has 5 and 1009 as its factors other than 1 and the number itself.

Hence, it is also a composite number.