Question

Explain why 3 x 5 x 7 x 11 + 11 is a composite number.​

Answer 1

Explanation:

take 11 common.. so you get

11 ( 3×5×7×1 +1)

11 ( 105+ 1)

11 (106)

11 × 2 × 53

hence there are more than 2 factors and so it is a composite no.

Answer 2

Composite number:- The number which has more than two factors is known as composite number.

$\mathfrak{\large{\underline{\underline{Given:-}}}}$

3 × 5 × 7 × 11 × 11

$\mathfrak{\large{\underline{\underline{To show:-}}}}$

It is a composite number.

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

3 × 5 × 7 × 11 + 11

Taking 11 as common.

$\implies$ $\bold{11 (3 × 5 × 7 × 1 + 1 ) }$

$\implies$ $\bold{11 ( 105 + 1 )}$

$\implies$ $\bold{11 × 106 }$

As we can see it has five prime factor 1, 11,2 and 53 ,106 .

Therefore it is a composite number.