Q. 64.3( 527 Votes )

Explain why 7 &#x

Answer :

Composite numbers are those numbers, which can be written in the form of the product of two or more integers, and at least one of them should not be 1 
(i)
7 × 11 × 13 + 13

= (7 × 11 × 13) + (13 × 1)

Taking 13 as common, we get,

= 13 × (7 × 11 + 1)
= 13 × (77 + 1)
= 13 × 78
= 13 × 13 × 6

As the given no is a multiple of two or more integers, one of them being other than 1.

Hence, it is a composite number.
Therefore, it is a composite number.


(ii)

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

= (7 × 6 × 5 × 4 × 3 × 2 × 1) + (5 × 1)

Taking 5 as common , we get,


= 5×(7×6×4×3×2×1+1)


= 5× (1008+1)


= 5×1009

As the given no is a multiple of two integers, one of them being other than 1.

Hence, it is a composite number.

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