Magic Rules to Test Divisibility by the Numbers 2 to 9

To save time when you're trying to find out if a number can be divided by another there are some simple tests that you can perform. These rules are fairly simple to remember, and might save you a lot of time depending on what kind of problem you are solving.

Divisibility is when you divide two numbers and get a remainder of zero. Examples are 6/2, and 10/5.

With that information let's start with the different rules to test divisibility.

To find out if a number is divisible, or can be divided by 2 you look at the last digit in the number. If this number can be divided by 2, then the whole number can be divided by 2. In 23954 you would look at 4, and thus 23954 is divisible by 2. You could also say that the remainder in this calculation would be zero because 4 divided by 2 is 2.

To find out if a number is divisible by 3 look to see if the sum of its digits is divisible by 3. If you have the number 4356 add up the digits 4+3+5+6=18, and know that 18/3=6. This means that 4356 is divisible by 3.

To find out if a number is divisible by 4, add up the last two digits to see if they are divisible by 4. In the number 56784 the last two digits would be 8 and 4, and the sum is 8+4=12. When you divide 12 with 4 you end up with 3, thus 56784 is divisible by 4.

To find out if a number is divisible by 5, see if the last digit is 0 or 5. The number 5670 ends with a 0, and is thus divisible by 5.

To find out if a number is divisible by 6, see if the last digit is even and that the sum of its digits can be divided with 6. The number 76524 ends with an even number, and has a sum of 7+6+5+2+4=24. Since 24 is divisible with 6 (24/6=4) and the number ends with an even number, 76524 is divisible with 6.

To find out if a number is divisible by 8, see if the last three digits are divisible by 8. To check for divisibility with 8 is a little more complex, however it can still save time. If we have the number 7744 you would check 744 and see if you could divide it with 8. The result is 968 thus 7744 is divisible with 8.

To find out if a number is divisible by 9, see if the sum of its digits is divisible by 9. Do exactly as you did with 3, except divide the sum you get by 9. If you have the number 7992 add them together 7+9+9+2=27. Divide 27 with 9 and get 3. Thus the number is divisible by 9.

These tricks are not necessary to know, but they can prove to be very helpful when solving math problems especially those including fractions. For the number 7 there is no simple rule, and it's therefore omitted.