# Rules of Divisibility Worksheets

The rules of divisibility help us to quickly determine if one number can go into another equally with having to do too much in the way of calculations. This will help you quickly process more advanced calculations and help you identify the best approach to take in many different mathematical situations. We cannot recommend stronger that you make do your best to remember these rules. When you get to algebra they will be invaluable for solving intricate equations and expressions. We listed all the provisions of the common uses of this rule set below. Students learn how to master basic division through the help of these worksheets. The lessons present the rules of divisibility in the form of tables that they will learn.

### Aligned Standard: 3.OA.C.7

- My First Table Step-by-Step Lesson- See if the integers are divisible. A ton of practice for you.
- Guided Lesson - This one will take a long time to complete. Just write "No", if they are not divisible.
- Guided Lesson Explanation - I give you a whole bunch of divisibility rules to get you started.
- Matching Sheet - This is great as a timed activity, this turns up the heat to critical thinking.
- Practice Worksheet - Some students say this takes 40 minutes. My intent was for this to be used over 5 days.
- Five Pack Of Practice - I still cannot believe that I got this all fit on one page.
- Using Divisibility Five Pack - Find the missing number to make each number sentence true or correct.
- Divisibility Five Pack - Determine if the number presented is divisible by the other numbers that we give you.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

You will see that we go up against divisibility from all angles on this one.

- Homework 1 - If a number can evenly divide (no remainders) into a number, that number is divisible by the other.
- Homework 2 - 36 ÷ 5 = 7 remainder 1 (No, the number cannot evenly divide.)
- Homework 3 - Circle the numbers below that are divisible by 5.

### Practice Worksheets

These charts really come in handy to work students through patterns too.

- Practice 1 - Match the tables and their answer keys. You can probably get away with just knowing six values for each table.
- Practice 2 - Write "Yes" if the number is divisible or "No" if number is not divisible by the given number.
- Practice 3 - Another test of divisibility. We approach a single integer with two prompts for you to evaluate.

### Math Skill Quizzes

We use number sentences and tables to test you on these skills.

- Quiz 1 - Use the clue to fill in the missing digit. You can approach this using a variety of methods. Use which ever one works best for you.
- Quiz 2 - Is the number to the left of each row divisible by the number at top of each column? Write YES or NO in each box.

### What are Divisibility Tables?

Divisibility means when a number is divided by another number the result is a whole number. For example, when 14 is divided by 7 the answer is 2 which means that the 14 is divisible by 7. On the other hand, when you divided 15 by 7 you will not get a whole number and the answer is 2 (1/7). Hence, this is not a whole number.

### The Rules of Divisibility

There are certain rules that are followed to check if a number is divisible by another. For instance, we can try dividing 723 by 3. But there is a way of checking if the division can lead to a whole number

7 + 2 + 3 = 12 | 12 / 3 = 4 (Yes)

Rule number 2, any integer which is not a fraction is divisible by 1.

For every number, there is a particular rule to be followed. It is represented below:

Rule for 2 - The last digit needs to be even (0, 2, 4, 6, 8).

Rule for 3 - The sum of digits needs to be divisible by 3. 381 (3 + 8 + 1 = 12) and (12 / 3 = 4).

Rule for 4 - The last 2 digits need to be divisible by 4. 1312 (12 / 4 = 3).

Rule for 5 - The last digit needs to be either 5 or 0.

Rule for 6 - Is the number even and divisible by 3? 114 (it is even and 1 + 1 + 4, 6 / 3 = 2).

Rule for 7 - Double the last digit and then subtracting it from the number made by other digits. The result has to be divisible by 7. 672 (double 2 is 4, 67 – 4 = 63 and 63 / 7 = 9)

Rule for 10 - If the value ends in 0 and is 10 or greater.

From here on, you are working with divisors that can be broken down into factors. An example of that would be a divisor of 12 (factors 3 and 4). If something is divisible by both 3 and 4, then it is divisible by 12 too.

### Tricks with Divisibility That Will Help You Master Tables Quickly

When we start working with these tables for the first time, they can be overwhelming. There are a simple tricks that you can use to help you through the first ten digits. Obviously, everything besides zero is divisible by one. This is why you will not see one listed on many tables at all. When evaluating the number two just remember that it can go evenly into any even number. Here is a neat trick to do with threes: find the sum of all the numbers in the value. If that sum is divisible by three, then so is the number. If the final two digits of a number are divisible by four, so is the number. Any number that ends in zero or five can be evenly divided by five. If a number is divisible by both two and three, it is divisible by six. There are advanced ways to evaluate sevens and eight, but we will not get into those now because they are pretty advanced. We will show you how to do this in our factor section. If a value ends in zero, it is divisible by ten. These tricks apply to values no matter how large or small that they are.