problem!

[gemini9525]

what's the trick for the remainder when divided by 6?

[bradp]

subtract large multiples of 6

234672 ---> 54672 ---> 672 ---> 72 --> remainder 0

[AuSmith]

Find the remainder when you divide by 3, call it R. From this remainder, you get two possibilities for the remainder when you divide by 6, namely R and R+3. Notice that one of R and R+3 is even and the other is odd. Since subtracting 6 does not change the oddness or evenness of the number, you must choose the one that matches the parity of the original number.

Ex1: 3265/6 has a remainder of ______.

Find R, the remainder when you divide by 3 by adding the digits together (casting out nines). 3+2+6+5=16. 16/3 has remainder 1. Therefore, 3265 has a remainder of 1 when divided by 3.

You know the answer is either R or R+3, that is 1 or 4. 3265 is odd, so you pick R because it's odd. [unparseable or potentially dangerous latex formula]

Ex2: 120110/6 has a remainder of ______.

Find R. 1+2+1+1=5. R=5-3=2.

Your answer is either 2 or 2+3=5. 120110 is even, so you pick 2 because it's even. [unparseable or potentially dangerous latex formula]