Question

prove that the product of any three consecutive positive integers is divisible by 6

Answer 1

Take 3 consecutive integers..

1,2,3 product =1*2*3=6 and 6 /6=1

Hence proved

Answer 2

Let, n be any positive integer.
so, The three consecutive integers will be n,n+1,n+2 respectively.
By Euclid division lemma,
a=6q+r, where, 0<_ r< 6
since, product of consecutive integers are as follows =6q×6q+1×6q+2
= 6 ( q × q+1 × q+2 )
= 6 ( (q)×q²+2q×q+3 )
= 6 ( q+2+3 )
= 6 ( q + 5)
= 6 / 6q = q = 1
Hence it is divisible by 6 for three consecutive integers n,n+1,n+2 respectively.
Hence proved .........
if you like Mark As BRAINLIST Answer.....
I hope it's help you ......
Thank you ......