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prove that product of evert three consecutive integers is always divisible by 3 as well as 2....
plzz help..
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4 Answers
5in 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
- Srijan Banerjee i have worked out this to 12
the product of every alternate no. is a multiple of 3 hope it helps :)Upvote·0· Reply ·2013-07-13 06:58:12
- Astha Gupta the concept that u presented about divisibility by 2...was nice..but the second thing...that is...about 12...i didn't get it...can u xplain way did u mean..????
- Astha Gupta i mean wat did u mean..n thanks in advance...
206For 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.
- Astha Gupta thanku sir....
- Sayantan Hazra welcome :)