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The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


Divisibility rules
Free lesson plan from HomeschoolMath.net

Do you remember? 

Numbers that are divisible by 2 end in  __, __, __, __, or __.

Numbers that are divisible by 5 end in either __ or __.

Numbers that are divisible by 10 end in __ .

 

Division rule for 3 is different.  No longer do we check in what the number ends:
  • If the sum of the digits of the number is divisible by 3, so is the number itself.

In other words, we add the digits of the number, and if that is divisible by 3, so is the original number.
 

Is 546 divisible by 3?  Yes, because 5 + 4 + 6 = 15, and 15 is divisible by 3.
Is 739 divisible by 3?   No, because 7 + 3 + 9 = 19, and 19 is not divisible by 3.

Example problems

1.  Check if these numbers are divisible by three.  Then divide the number by 3 in your notebook and record the answer here.  What is the remainder if the number IS divisible by 3?

Number  sum of its digits

 divisible by 3
(yes/no)

division result
771

8096

2304

    771 ÷ 3 = ___, R ___

8096 ÷ 3 = ___, R ___

2304 ÷ 3 = ___, R ___

 

Division rule for 9 is similar to the division rule for 3.
  • If the sum of the digits of the number is divisible by 9, so is the number itself.
Is 546 divisible by 9?    No, because 5 + 4 + 6 = 15, and 15 is not divisible by 9.
Is 738 divisible by 9?    Yes, because 7 + 3 + 8 = 18, and 18 is divisible by 9.

 

2.  Check if these numbers are divisible by nine.  Then divide the number by 9 in your notebook and record the answer here.  What is the remainder if the number IS divisible by 9?  

 

Number  sum of its digits

 divisible by 9
(yes/no)

division result
771

1000

333

    771 ÷ 9 = ___, R ___

1000 ÷ 9 = ___, R ___

333 ÷ 9 = ___, R ___

 


3.  Use the divisibility rules and check if the number is divisible by 2, 3, 5, or 9. 

 

divisible by    divisible by   
Number   2    3    5   9  Number   2    3    5    9 
238

6095

                     477

5770

       

 

Division rule for 6 says
  • If the number is divisible by 2 and by 3, it is divisible by 6.

 

4.  Check if these numbers are divisible by six.  If it is, then divide the number by 6 in your notebook and record the answer here.  

Number

 divisible by 6
(yes/no)

division result
771

8196

1000

  771 ÷ 6 = ___, R ___

8196 ÷ 6 = ___, R ___

1000 ÷ 6 = ___, R ___

 

5.  a)  Find two numbers that are divisible by both 10 and 3.

     b)  Find two numbers that are divisible by both 2 and 9.

 

continue to factoring

 

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Learn...
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