Question

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

Answer 1

Answer:

7 x 11 x 13 + 13

We can also write this as

⇒ (77 + 1) x 13

⇒ 1014

So the factors are

⇒ 13 x 13 x 3 x 2

It is a composite number. The given number has more than two factors.

Now consider

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

We can also write it as

⇒ 5(7 x 6 x 5 x 4 x 3 x 2 x 1 + 1)

By calculation we get

⇒ 1009 x 5

It is a composite number. The given number has more than two factors.

Step-by-step explanation:

Answer 2

By definition,  

A composite number is a positive integer that has a factor other than 1 and itself. Now considering your numbers,

7×11×13+13 may be written as, 13 x [(7 x 11) + 1]  i.e. 13 x (78). So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78 = 39 x 2. So, 39 and 2 are also it's factors. So this number is definitely not prime. Hence its composite number.

Similarly, 7×6×5×4×3×2×1+5 can be written as 5 x [ (7 x 6 x 5 x 4 x 3 x 2 x 1) +1]  , i.e. 5 x (1009). So, other than the number and 1, it have 5 and 1009 as it's factors too. So it is also a composite number.