Numbers

Numbers are fun! I just bought a book of random facts on numbers, there is one in particular that gave me a new perspective on the way my mind works. It is a question asking which one of these following numbers is divisible by 3:

281, 354, 962, 3742, or 138624147.

Normally, I think that I would picture solving it in my mind visualising the symbols often used in division problems done on paper. I realized this is not the case in my mind. I see it much like this.

3 (into) 281
3, 28, 9, 27, 11, 9, 3, 20, 6, 30, 10, .10 (equals) 96.1

or

3 (into) 354
3, 3, 1, 5, 1, 2, 24, 8 (equals) 118

this works well for smaller numbers, but the larger ones are a bit more confusing.

3 (into) 1386241417
3, 13, 4, 18, 6, 2, 8, 4, 7, 5, 20, 18, 6, 20, 18, 6, 18, 20, 6, 18, 6 (or god this is going to go on for ever) (equals) 4628475.66666666.......

Does anyone else visualize division problems like this in their mind? If not, how do you do it?