Learning the divisibility rules is an important part of basic mathematics. To help you get a handle on them, these worksheets include step-by-step instructions along with explanations and questions and answers for each rule from 2 to 12.

Divisibility rules for numbers 2 to 12 with examples:

Divisibility by 2: A number is divisible by 2 if its units digit is even (0, 2, 4, 6, or 8). Example: 632 is divisible by 2 because its units digit is 2.

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. Example: 315 is divisible by 3 because 3 + 1 + 5 = 9, which is divisible by 3.

Divisibility by 4: A number is divisible by 4 if its last two digits form a number that is divisible by 4. Example: 736 is divisible by 4 because 36 is divisible by 4.

Divisibility by 5: A number is divisible by 5 if its units digit is either 0 or 5. Example: 350 is divisible by 5 because its units digit is 0.

Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3. Example: 894 is divisible by 6 because it is divisible by 2 and the sum of its digits is divisible by 3 (8 + 9 + 4 = 21, which is divisible by 3).

Divisibility by 7: If the last digit of the number is doubled and subtracted from the rest of the number and this difference is divisible by 7. Example

315, Double the last digit 5 X 2 = 10

Subtract rest of the number by 10 = 31 -10 = 21

And 21 is divisible by 7, therefore 315 is divisible by 7.

Divisibility by 8: A number is divisible by 8 if its last three digits form a number that is divisible by 8. Example: 1736 is divisible by 8 because 736 is divisible by 8.

Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Example: 207 is divisible by 9 because 2 + 0 + 7 = 9, which is divisible by 9.

Divisibility by 10: A number is divisible by 10 if its units digit is 0. Example: 940 is divisible by 10 because its units digit is 0.

Divisibility by 11: There is a simple rule for determining whether a number is divisible by 11: alternate adding and subtracting digits from left to right. If the resulting number is divisible by 11, then the original number is also divisible by 11. Example: 9463 is divisible by 11 because 9 - 4 + 6 - 3 = 8, which is divisible by 11.

Divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4. Example: 360 is divisible by 12 because it is divisible by 3 and its last two digits form a number that is divisible by 4.

Questions and Answers Practice Sheet on Divisibility Rules from 2-12.

With this divisibility rule worksheet, you are given a set of 20 questions ranging from basic to more complex. It takes a multi-step approach for each question within each range in order familiarize you with the various rules. First, it will ask easier questions which require identifying if some numbers are divisible by another number in the range specified. Following that, you must answer more complex problems which involve pairs of two different numbers and whether one is divisible by the other or not. This practice sheet provides step-by-step explanations and examples to give you an understanding of why each section works to inform your answers better. All those combined make this an ideal resource for mastering comprehensive knowledge on divisibility rules in mathematics.