You probably already know that the last digit in the product of two numbers depends only on the last digits of the numbers being multiplied. For example, if one number ends in 7 and another in 2, when they are multiplied the last digit will be 4.

It did not occur to me until I saw it mentioned, that the same holds true for the last 2 digits, last 3 digits and so on. For example 11×13 = 143. It therefore follows that 211×513 must end with 43, which it does. 211×513=108,243.

If you write out a multiplication, you can see how this works. If you know modular arithmetic, the proof is immediate.

I can’t think of any practical use for this, but it might be a fun thing to teach in elementary school when students learn multiple digit multiplication.