Mastering Divisibility Rules for 2 - 15: What You Need To Know By: Teacher Virgie

    

Mastering Divisibility Rules for 2 - 15: What You Need To Know

DIVISIBILITY RULES

By: Teacher Virgie

         Understanding divisibility rules is like having a secret code to unlock the mysteries of numbers. These rules provide a shortcut to determine if a number is divisible by another without the need for complex calculations. In this blog, we'll delve into the fascinating world of divisibility rules, demystifying the process and showcasing how these rules can simplify your mathematical journey.

   Let us now explore the different divisibility rules/tests! You may notice some similarities among the rules.

Divisibility by 2: The Rule of Evenness

• Any number ending in 0, 2, 4, 6, or 8 is divisible by 2.

Examples: 
34              

46              

98              

200            

502

Divisibility by 3: The Sum Rule

• The sum of a number's digits determines its divisibility by 3.

Examples: 
39 = 3 + 9 = 12, so 39 is divisible by 3

1563 = 1 + 5 + 6 + 3 = 15, so 1563 is divisible by 3

Divisibility by 4: The Last Two Digits Rule

• If the last two digits of a number are divisible by 4, the entire number is divisible by 4.

Example: 
4564

64 is the last digit and it's divisible by 4 and 4564 is divisible by 4.

Divisibility by 5: The Ending in 0 or 5 Rule

• Any number ending in 0 or 5 is divisible by 5.

Examples: 
205              

380           

200            

505          

1440

Divisibility by 6: The Combination Rule

• If a number is divisible by both 2 and 3, it is divisible by 6.

Example: 
504

The last digit of 504 is 4, so it's divisible by 2.

Find the sum of all digits of 504 if it is divisible by 3. 

5 + 0 + 4 = 9 and 9 is divisible by 3.

Since both divisible by 2 and 3; therefore 504 is divisible by 6.

Divisibility by 9: The Sum Rule Revisited

• Similar to divisibility by 3, the sum of a number's digits determines its divisibility by 9.

Examples: 
1539 = 1 + 5 + 3 + 9  = 18, so 1539 is divisible by 9

8964 = 8 + 9 + 6 + 4 = 27, so 8964 is divisible by 9

Divisibility by 10: The Ending in 0 Rule

• Any number ending in 0 is divisible by 10.

Examples: 
200              

380           

200            

500          

1440

Divisibility by 11: Difference between The Alternating Sums Rule

• Difference between the alternating sums of a number's digits determines its divisibility by 11.

Example: 
17490

Find the alternating sum of a number's digits starting from right to left

1 + 4 + 0 = 5

7 + 9 = 16

16 - 5 = 11

Hence, 17490 is divisible by 11.

Divisibility by 12: The Combination of 3 and 4

• If a number is divisible by both 3 and 4, it is divisible by 12. 

Divisibility by 14: The Combination of 2 and 7

• If a number is divisible by both 2 and 7, it is divisible by 14. 

Divisibility by 15: The Combination of 3 and 5

• If a number is divisible by both 3 and 5, it is divisible by 15. 

      Mastering divisibility rules is like having a powerful toolkit for navigating the world of numbers. By understanding and applying these rules, you not only simplify mathematical calculations but also develop a deeper appreciation for the inherent patterns and logic within the realm of mathematics. So, embrace the divisibility rules, unlock the secrets of numbers, and elevate your math prowess to new heights!

WORKSHEET ON DIVISIBILITY RULES

BY: TEACHER VIRGIE

ANSWER KEY

BY: TEACHER VIRGIE

Leave  a comment if you have any questions. 

Thank you.