Question

Prove that the product of 3 consecutive positive integer is divisible by 6.

Answer 1

Hey,

Let the three consecutive positive integers are: n, (n+1)and (n+2)

Product = n*(n+1)* (n+2)

Let n=1

product = 1*(1+1)* (1+2)

            = 1*2*3

            = 6

So product is divisible by 6

Again let n=2

product = 2*(2+1)* (2+2)

            = 2*3*4

            = 24

So product is divisible by 6

Again let n=3

product = 3*(3+1)* (3+2)

            = 3*4*5

            = 60

So product is divisible by 6.

HOPE IT HELPS:-))

Answer 2

Answer:

Hey,

Let the three consecutive positive integers are: n, (n+1)and (n+2)

Product = n*(n+1)* (n+2)

Let n=1

product = 1*(1+1)* (1+2)

           = 1*2*3

           = 6

So product is divisible by 6

Again let n=2

product = 2*(2+1)* (2+2)

           = 2*3*4

           = 24

So product is divisible by 6

Again let n=3

product = 3*(3+1)* (3+2)

           = 3*4*5

           = 60

So product is divisible by 6.

HOPE IT HELPS:-))

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