Question

prove that the product of three consecutive positive integer is divisible by 6
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Answer 1

let the three positive consecutive integers be = x, x+1, x+2..

x (x+1)(x+2)

4xsq.+2x

2 (2xsq.+ x )

2m ........ (2xsq. + x = m)

2m is divisible by 6 ..

HENCE PROVED

Answer 2

Let the three consecutive positive integers be x,x+1 and x+2

×+×+1+×+2=6÷×

3x+3=6÷x

3x×x=6-3

3x^2=3

x^2=1

x=1

therefore x=1

x+1=2

x+2=3

As 1+2+3=6

and 6÷6=1

Hence they are divisibled by 6 without any remainder