Question

Explain why 7 x6x5x4 x 3x2x1 +5 are composite numbers.​

Answer 1

6 is composite, since it is divisible by 1, 2, 3 and even 6.

Now consider

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.

Hence proved

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