Division Tricks

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How can you find out whether a given large number is divisible by another number without remainder?

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Division Tricks

How can you quickly know if one number will divide evenly into another number, leaving no remainder? This subject will be very boring when it comes large numbers if we don't know some tricks. So, now I'm going to tell you some shortcuts. Well, here are they.

Division by 2
Very simple. Any number that ends in 0,2,4,6 or 8 can divisible by 2 without remainder.

Division by 3
Add the number's digits. Keep adding numbers until one digit remains. If the answer is 3, 6 or 9 then the number will divisible by 3 without remainder.

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.

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

Division by 6
Add up the digits until one digit remains and see if the sum is 3, 6 or 9. If it is, check the number's last digit. If it is an even number then, the original number is evenly divisible by 6.

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 784. 4 x 2 = 8. 78 - 8 = 70. 70 is evenly divisble by 7. So 784 is also!
Note : This is not a very easy way when it comes to very large numbers.

Division by 8
If the number's last 3 digits are 000 or if it is a 3-digit number evenly divisible by 8, then the number itself is divisible by 8.

Division by 9
Sum the number's digits until one digit remains. If the answer is 9, then the original number is also divisible by 9 without remainder.

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

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

If the number is a 3 digit number, add the two outside digits. If the difference between the sum and the middle digit is 11 then 11 divides evenly into the 3 digit number. If the sum is the same as the middle digit, then 11 will also divide evenly into the number. Try 484. 4 + 4 = 8 which equals the middle digit so 11 divides into 484 evenly. How about 913? 9 + 3 = 12 and 12 - 1 = 11 so 913 is evenly divisible by 11.

If the number is more than 3 digit number, add odd position's numbers together, starting with the first position. Then, add the even position's numbers together, starting with the second. If the both answers are same the original number is divisible by 11. Try 142065. 1+2+6 = 4+5, therefore it should divide evenly by 11.


Add odd position's numbers and even position's numbers as the above example. Subtract the smaller number from the larger. If the difference is evenly divisible by 11, original number is also divisible by 11. Take the number 181,907. The numbers 8,9, and 7 are in the even positions. They sum to 24. The numbers 1,1, and 0 are in the odd positions. They sum to 2. Subtract 2 from 24 to get 22. 22 divides by 11 into 2, so 181,907 is evenly divisible by 11.


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 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.

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