Divisibility Worksheet Practice

Introduction to Divisibility Rules

To solve divisibility problems, it’s essential to understand the rules that govern whether a number can be divided by another without leaving a remainder. These rules are straightforward and can be applied to various numbers. In this section, we will explore the most common divisibility rules, including those for 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Divisibility Rules for Common Numbers

Let’s break down the divisibility rules for each of these numbers: - 2: A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). - 3: A number is divisible by 3 if the sum of its digits is divisible by 3. - 4: A number is divisible by 4 if the last two digits form a number that is divisible by 4. - 5: A number is divisible by 5 if its last digit is either 0 or 5. - 6: A number is divisible by 6 if it is divisible by both 2 and 3. - 7: A number is divisible by 7 if you double the last digit and subtract this value from the remaining digits. If the result is divisible by 7, then the original number is also divisible by 7. - 8: A number is divisible by 8 if the last three digits form a number that is divisible by 8. - 9: A number is divisible by 9 if the sum of its digits is divisible by 9. - 10: A number is divisible by 10 if its last digit is 0.

Applying Divisibility Rules

To apply these rules, let’s consider a few examples: - Is 48 divisible by 2, 3, or 6? - By 2: Yes, because 48 ends in 8, which is an even number. - By 3: Yes, because 4 + 8 = 12, and 12 is divisible by 3. - By 6: Yes, because it meets the criteria for both 2 and 3. - Is 75 divisible by 5? - Yes, because 75 ends in 5.

Practice Exercises

Here are some practice exercises to help you master the divisibility rules: - Determine if the following numbers are divisible by 2, 3, 4, 5, 6, 7, 8, 9, or 10: - 120 - 93 - 48 - 25 - 17 - Check if 216 is divisible by 2, 3, 4, 6, 8, or 9. - Identify which of the following numbers are divisible by 7: 14, 21, 35, 49, 63.

Solving Divisibility Problems

Solving divisibility problems involves applying the rules mentioned above. Let’s solve a few examples: - Is 432 divisible by 4? - Yes, because the last two digits (32) form a number that is divisible by 4. - Is 945 divisible by 9? - Yes, because 9 + 4 + 5 = 18, and 18 is divisible by 9.

📝 Note: Practicing these problems regularly will help you become more proficient in applying divisibility rules.

Using Tables for Divisibility

Sometimes, using a table can help organize the information and make it easier to identify patterns or apply rules. Here’s an example table for the divisibility rules of 2 through 10:

Number	Divisibility Rule
2	Last digit is even (0, 2, 4, 6, 8)
3	Sum of digits is divisible by 3
4	Last two digits form a number divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
7	Double the last digit, subtract from the remaining digits; result is divisible by 7
8	Last three digits form a number divisible by 8
9	Sum of digits is divisible by 9
10	Last digit is 0

Conclusion and Final Thoughts

Mastering divisibility rules is a fundamental aspect of mathematics that simplifies various calculations and problem-solving tasks. By understanding and applying these rules, individuals can enhance their mathematical proficiency and tackle more complex problems with confidence. Remember, practice is key to becoming proficient in divisibility rules, so be sure to work through numerous exercises to solidify your understanding.