# How do you show that the product of #3# consecutive integers is always divisible by #6# ?

##### 1 Answer

Apr 30, 2016

#### Answer:

See explanation...

#### Explanation:

Consider three consecutive integers:

#n = 3q+r#

for some integer quotient

If

If

If

So at least (in fact exactly) one of

Hence

Similarly for

#n = 2q_1+r_1#

for some integer quotient

If

If

So at least one of

Hence