Divisibility Rules

Dividing by "6"

A number is divisible by 6 if it is also divisible by 2 and 3.

Dividing by "3"

Add all the digits in the original number. If the sum is divisible by 3, so is the original number. Example: 12,123 (1 + 2 + 1 + 2 + 3= 9). Since 9 is divisible by 3, 12,123 is divisible by 3, also.

Dividing by "2"

All even numbers are divisible by 2. Even numbers have 0, 2, 4, 6, or 8 in the "ones" place.

Dividing by "7" Test 2

Beginning with the ones column, multiply the ones digit by 1, the tens digit by 3, the hundreds digit by 2, the thousands digit by 6, the tentousands digit by 4, and the hundred thousands digit by 5. Repeat this sequence of multipliers (1,3, 2, 6, 4, 5), if the original number has more than 6 digits. Add the products of these numbers, and if the sum is divisible by 7, so is the original number. Example: Is 2,016 divisible by 7? 6(1) +1(3) +0(2) +2(6) = 21. 21 is divisible by 7, so 2,016 is also divisible by 7.

Dividing by "7" Test 1

Double the digit in the ones place, then subtract this number from the remaining digits in the number. If the difference is divisible by 7, then the whole number is divisible by 7. Example: For the number 357, double the 7 to = 14. Subtract 14 from 35 to =21. Since 21 is divisible by 7, then 357 is divisible by 7.

Dividing by "10"

If a number has a 0 in the ones place, it is divisible by 10.

Dividing by "8"

If the last 3 digits are evenly divisible by 8, so is the original number. Example: For the number 6,328, 328 is evenly divisible by 8, so 6,328 is divisible by 8.

Dividing by "4"

If the last two digits in the original number (the hundreds and ones places) are divisible by 4, then the entire number is too. Example: 356,912 is divisible by 4, because 12 is divisible by 4.

Dividing by "12"

If the sum of the digits is divisible by both 3 AND 4, the original number is divisible by 12

Dividing by "11"

If you add every second digit and then subtract the sums of all the other digits and the answer is 0 or divisible by 11, the original number is divisible by 11. Examples: 1364 (3+4)-(1+6)=0, so 1364 is divisible by 11. 3729 (7+9)-(3+2)=11, so 3729 is divisible by 11. 25,176 (5+7)-(2+1+6)=3, so 25,176 is NOT divisible by 11.

Dividing by "5"

Numbers that have a 5 or a 0 in the ones place are divisible by 5.

Dividing by "9"

The rule is almost the same as dividing by 3. Add up all the digits. If the sum is divisible by 9, so is the original number. Example: For 43, 785, add 4 + 3 + 7 + 8 + 5 =27. 27 is divisible by 9, so 43,785 is also divisible by 9.