Question

Explain whether 3 x 12 x 101 + 4 is a prime number or a composite number

Answer 1

Hi ,

* Every composite number has atleast three factors.

*Every prime number has only two factors.

Now ,

3 × 12 × 101 + 4

= 3 × 3 × 4 × 101 + 4

= 4 [ 3 × 3 × 101 + 1 ]

= 4 × k [ where k = 3 × 3 × 101 + 1 ,

Some integer ]

= 4 × k × 1

= composite number

[ it has more than two factors 4 , k ,and 1 ]

Therefore ,

3 × 12 × 101 + 4 is a composite number.

I hope this helps you.

:)

Answer 2

= 3 × 12 × 101 + 4 = 4(3 × 3 × 101 + 1)

             

= 4(909 + 1)

             

= 4(910)

             

= 2 × 2 × 2 × 5 × 7 × 13

           

=Composite number

(Product of more than two prime factors)