...?????? HOW TO PROVE..????

prove that product of evert three consecutive integers is always divisible by 3 as well as 2....
plzz help..

4 Answers

269
Astha Gupta ·

i mean every

5
Srijan Banerjee ·

in every three consecutive integers there will always be an even no. and the product of any no. with an even no. will give an even no. and so it is divisible by 2
i can't prove why is it divisible by 3 :P

5
Srijan Banerjee ·

sorry that theory was wrong i just worked it out again :P

206
Sayantan Hazra ·

For 3 consecutive integers, there will be atleast 1 even number, so it is divisible by 2

When you divide anything by 3, you can obtain either of 0, 1, 2 as remainders.
For 3 consecutive integers, if you divide them one by one, you are bound to get either of 0, 1, 2 as remainders. Hence, there is atleast 1 number which gives you 0 when divided by 3.
Thus, there will be atleast 1 number in the three consecutive integers which is divisible by 3.

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