Question

Explain why 7 * 11 * 13 + 13 and
7 6 * 5 * 4 * 3 * 2 * 1 + 5 are composite numbers ?
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Answer 1

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Step-by-step explanation:

1.) 7 × 11 × 13 + 13

(common out)

13 ( 7× 11 × 1 + 1)

13 ( 77 × 1 + 1 )

13 ( 77 + 1 )

13 ( 78 )

Answer:- 1014

Now, LCM

1014 = 2^1 × 3^1 × 13^2

If LCM is come in prime Factor

Then,7 × 11 × 13 + 13 is Composite Number.

2.) 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

(common out)

5 ( 7 × 6 × 1 × 4 × 3 × 2 + 1 )

5( 1008 + 1 )

5 ( 1009 )

Answer:- 5045

Now, LCM

5045 = 5^1 × 1009^1

( 1009 is a Prime Number. )

If LCM is come in prime Factor

Then,7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is Composite Number.

Answer 2

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