A trick to multiply two large numbers and amaze students or other people

Students choose a three-digit number
    He chooses another number (143)
    ... and all to multiply on the board: prepared, ready, now!

Naturally, the wise teacher always wins. The trick is more or less simple - or not so much, it depends on how you look at it - and it has to do with the chosen number. It also requires a bit of mental calculation.

The thing works like this: it turns out that 143 × 7 = 1001. And it is known that when a three-digit number is multiplied by 1001 the result is the same number "repeated twice"; in example 953 it would be 953953. But if you divide 953953/7 (or seen in another way, 953 × 1001/7) it is easy to see that the result is the one that arises: 953 × 143.

So the mental trick is to mentally divide 953953 by 7. Something that may have more or less difficulty but that by fixing the gaze and putting "concentration face" can be done in a few seconds. The result always gives exact.