Show that positive integers is divisible by 6, Mathematics

Show that the product of 3 consecutive positive integers is divisible by 6.

Ans:

n,n+1,n+2 be three consecutive positive integers

We know that n is of the form 3q, 3q +1, 3q + 2

So we have the following cases

Case - I     when n = 3q

In the this case, n is divisible by 3 but n + 1 and n + 2 are not divisible by 3

Case -  II   When n = 3q + 1

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3

Case - III When n = 3q +2

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3

Hence one of n, n + 1 and n + 2 is divisible by 3

Posted Date: 4/8/2013 1:08:27 AM | Location : United States







Related Discussions:- Show that positive integers is divisible by 6, Assignment Help, Ask Question on Show that positive integers is divisible by 6, Get Answer, Expert's Help, Show that positive integers is divisible by 6 Discussions

Write discussion on Show that positive integers is divisible by 6
Your posts are moderated
Related Questions
A retired couple has up to $30000 to invest in fixed-income securities. Their broker recommends investing in two bonds: one a AAA bond yielding 8%; the other a B+ bond paying 12%.

Evaluate the volume of a ball whose radius is 4 inches? Round to the nearest inch. (π = 3.14) a. 201 in 3 b. 268 in 3 c. 804 in 3 d. 33 in 3 b. The volume of a

If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans:    d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,

Q. How to plot Line Graphs? Ans. Line graphs can be useful in analyzing data. They are particularly helpful when you are interpolating or extrapolating information from y

If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans:    p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (

How many relations are possible from a set A of 'm' elements to another set B of 'n' elements?     Ans: A relation R from a set A to other set B is specified as any subset of A

The sum of the diameters of two circles is 2.8 m and their difference of circumferences is 0.88m. Find the radii of the two circles  (Ans: 77, 63) Ans:    d 1 + d 2 = 2.8 m=

Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po

Mathematical Formulae (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab (a + b) 2 +

Find out all the numbers c that satisfy the conclusions of the Mean Value Theorem for the given function.                                               f ( x ) = x 3 + 2 x 2 -