When we add up the digits of a number and the result is divisible by 3, then the number is divisible by 3. If, when we add the digits together we end up with a double digit number, we add the digits again and see if the result is divisible by 3. If it is, then so is the number. So 555 is divisible by 3 because 5+5+5=15=1+5=6. 555531 is also divisible by 3: 5+5+5+5+3+1=24=2+4=6. There are similar tricks for 9, 6 (if number is even and satisfies the 3 test), 11 (add alternate digits and subtract results), and you can use the 9's remainder for checking arithmetic (the 9's remainder is the result of adding all the digits until you get just one digit): 49*73=3577. 4+9=13, 1+3=4; 7+3=10, 1+0=1; 3+5+7+7=22, 2+2=4; multiply the 9's remainders: 4*1=4. 49+73=122=1+2+2=5; 4+1=5. Good, isn't it?