How can you quickly know if one number will divide evenly into another number, leaving no remainder? For example, will 3 divide evenly into 2,169,252? Well, I wouldn't have brought the subject up if I didn't know some curious shortcuts.I think all of you know  the division by 2 ,5 ,10  . Now we learn   division by every possible number

Division by 2
No surprise here. Any number that ends in 0,2,4,6 or 8 is evenly divisible by 2.

Division by 3
Add the number's digits. If the sum is evenly divisible by 3, then so is the number. So, will 3 divide evenly into 2,169,252? Yes it will, because the sum of the digits is 27, and 27 is divisble by 3. If you want, you can keep adding numbers until one digit remains. For example, keep going with 27. 2 + 7 = 9, which is also evenly divisible by 3.

Division by 4
If the number's last 2 digits are 00 or if they form a 2-digit number evenly divisible by 4, then number itself is divisible by 4. How about 56,789,000,000? Last 2 digits are 00, so it's divisible by 4. Try 786,565,544. Last 2 digits, 44, are divisible by 4 so, yes, the whole number is divisible by 4.

Division by 5
Any number that ends in a 0 or 5 is evenly divisible by 5. Easy enough.

Division by 6
The number has to be even. If it's not, forget it. Otherwise, add up the digits and see if the sum is evenly divisible by 3. It it is, the number is evenly divisible by 6. Try 108,273,288. The digits sum to 39 which divides evenly into 13 by 3, so the number is evenly divisible by 6. If you want, you can keep adding numbers until only one digit remains and do the same thing. So in this case, 3 + 9 = 12 and 1 + 2 = 3, and 3 is evenly divisible by 3!

Division by 7
Multiply the last digit by 2. Subtract this answer from the remaining digits. Is this number evenly divisible by 7? If it is, then your original number is evenly divisible by 7. Try 364.       4, the last digit, multiplied by 2 = 8. 36, the remaining digits, minus 8 = 28. The last time I checked, 28 is evenly divisble by 7, and thus, so is 364!
Another example   1792   2 is the last  digit  multiply it by 2and subtract  it  from original number
        1792
           -4
       1 7 5       repeat once again 5x2=10
     - 10     
           7         7 is divisible by 7 so  is 1792

Division by 8
If the number's last 3 digits are 000 or if they form a 3-digit number evenly divisible by 8, then the number itself is divisible by 8. How about 56,789,000,000? Last 3 digits are 000, so it's divisible by 8. Try 786,565,120. The last 3 digits, 120, divide by 8 into 15, so yes, the whole number is divisible by 8.

Division by 9
Sum the number's digits. If it divides by 9, you're in luck. As with the tests for 3 and 6, you can keep adding numbers until you're left with only one digit.  9873    , 9+8+7+3=27 =2+7 =9  9873 is divisible by 9

Division by 10
Any number that ends in 0 is evenly divisible by 10.

Division by 11
Here are four ways for different types of numbers:

Division by 12
If the number can be evenly divided by 3 and 4, the same can also be said for 12. Use the methods for Division by 3 and Division by 4 above. If they both work, your number is also evenly divisible by 12.

Division by 13
 Multiply the last digit  by 4 and add it from remaining digits Is this number evenly divisible by 13? If it is, then your original number is evenly divisible by 13. Try 598
        598
     +32       (8x4=32)
      9  1        Repeat once again
 +  4     
     13    so it is divisible by 13

Division by 15
If the number can be evenly divided by 3 and 5, the same can also be said for 15. Use the methods for Division by 3 and Division by 5 above. If they both work, your number is also evenly divisible by 15.

 Division by 17

Multiply the last digit by 5. Subtract this answer from the remaining digits. Is this number evenly divisible by 17? If it is, then your original number is evenly divisible by 17. Try 663
             663
         -  15
             51      it is divisible by 17 so 663 is divisible by 17

 Division by 19

Multiply the last digit by 2. Add this answer from the remaining digits. Is this number evenly divisible by 19? If it is, then your original number is evenly divisible by 19. Try 741
             741
       +      2
             76    
        + 12
          19     it is divisible by 19 so 741  is divisible by 19

 Division by 23

Multiply the last digit by 7. Add this answer from the remaining digits. Is this number evenly divisible by 23? If it is, then your original number is evenly divisible by 23. Try 667
             667
       +    47
           113  
        + 21
          23    it is divisible by 23 so 667  is divisible by 23

Division by 24
If the number can be evenly divided by 3 and 8, the same can also be said for 24. Use the methods for Division by 3 and Division by 8 above. If they both work, your number is also evenly divisible by 24.

 Division by 29

Multiply the last digit by 3. Add this answer from the remaining digits. Is this number evenly divisible by 29? If it is, then your original number is evenly divisible by 19. Try 667
             667
       +   21
             87    
        + 21
          29    it is divisible by 29 so 667  is divisible by 29

 Division by 31

Multiply the last digit by 3. Subtract this answer from the remaining digits. Is this number evenly divisible by 31? If it is, then your original number is evenly divisible by 31. Try 744
             744
       -    1 2
             62    
             6
          0     it is divisible by 31 so 744  is divisible by 31

Division by 33
If the number can be evenly divided by 3 and 11, the same can also be said for 33. Use the methods for Division by 3 and Division by 11 above. If they both work, your number is also evenly divisible by 33.

Division by 37