Question

Explain why the following are composite number:-
(1). 11×13×15×17+17
(2). 7×6×5×4×3×2×1+5
(3). 11×13×17×19-17

Answer 1

As we know that composite no. are those no. which have more factors other than 1 .So,

1- 11×13×15×17+17

Take 17 common in this whole digits

17( 11×13×15×1+1)

17( 2145+1)

17( 2146)

17× 2146 = 36482

Now the factors of 36482= 2× 18241

Here we can see that 36482 have more factor other than 1 . Hence it is a composite no.

Similarly In 2nd - 7×6×5×4×3×2×1+5

Take 5 as common

= 5( 7×6×1×4×3×2×1+1)

= 5(1008+1)

= 5× 1009 = 5045

Factors of 5045 = 5× 1009

Hence it is a composite no.because it also have more factor other than 1

Now in 3rd- 11×13×17×19-17

Take 17 common

= 17(11×13×1×19-1)

= 17 ( 2717-1)

= 17× 2716 = 46176

Factors of 46176= 2×2×2×2×2×2×2×2×3...

It is also a composite no. because it have more factor other than 1

Answer 2

Step-by-step explanation:

We have,

→ ( 17 × 11 × 2 ) + ( 17 × 11 × 5 ) .

= ( 17 × 11) ( 2 + 5 ).

== ( 17 × 11 × 7 ) = x [ Let ].

Thus, the number x has 3 factors i.e., 17 × 11 × 7.

And, we know that composite numbers are those numbers who have more than 2 factors.

Therefore, the number x is a composite number as it has 3 factors.

Hence, it is solved.