CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution

Let n be any positive integer is of the form 6q or, 6q+1 or, 6q+2 or, 6q+3 or, 6q+4 or, 6q+5.
If n=6q, then
n(n+1)(n+2)=6q(6q+1)(6q+2), which is divisible by 6

If n=6q+1, then
n(n+1)(n+2)=(6q+1)(6q+2)(6q+3)=6(6q+1)(3q+1)(2q+1),
which is divisible by 6.

If n=6q+2, then
n(n+1)(n+2)=(6q+2)(6q+3)(6q+4)=12(3q+1)(2q+1)(2q+3),
which is divisible by 6.

Similarly , n(n+1)(n+2) is divisible by 6 if n=6q+3 or, 6q+4 or, 6q+5.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Divisible by 2 or 5 or Both
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon