Question

5)Explain why (7x13x11)+11 &(7x6x5x4x3x2x1)+3 is composite number?

Answer 1

Given 7×11×13+13

=13×(7×11+1)=3×78

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

similarly in

7×6×5×4×3 ×2×1+5

=5(7×6×4×3 ×2×1+1)=5×1009

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

This answer is from my textbook just I edited the numbers.

I surely hope that this will help you

Answer 2

Answer:

7 x 13 x 11 + 11                                       (7 x 6 x 5 x 4 x 3 x 2 x 1) + 3

= (7 x 13 + 1) x 11                                    = (7 x 6 x 5 x 4 x 2 x 1 + 1) x 3

= (91 + 1) x 11                                           = (1680 + 1) x 3

= 92 x 11.                                                 = 1681 x 3

= (2 x 2 x 23) x 11                                     = (41 x 41) x 3

= 2 x 2 x 11 x 23                                       = 3 x 41 x 41

By fundamental theorem of arithmetic both these numbers can be expressed as the product of its primes. So they are composite.