Wednesday, April 20, 2016

Divisibility Method


Direct Method of  Divisibility


Rule 1: (Divisibility by 2) :  If the last digit is even (0.2,4,6,8), the number is divisible by 2.

Rule 2: (Divisibility by 3) :  If the sum of the digits is divisible by 3, the number is also divisible by 3.

Rule 3: (Divisibility by 4) :  If the last two digits form a number divisible by 4, the number is also divisible by 4.

Rule 4: (Divisibility by 5) :  If the last digit is a 5 or a 0, the number is divisible by 5.

Rule 5: (Divisibility by 6) :  If the number is divisible by both 3 and 2, it is also divisible by 6.

Rule 6: (Divisibility by 8) :  If the last three digits form a number divisible by 8, then so is the whole number divisible by 8.

Rule 7: (Divisibility by 9) :  If the sum of the digits is divisible by 9, the number is also divisible by 9.

Rule 8: (Divisibility by 10) :  If the last digit is 0 , the number is divisible by 10.

Rule 9: (Divisibility by 11) :  Alternately add and subtract the digits from left to right. If the result is 0 or divisible by 11, the number is also divisible by 11.
                    Example :
                                      to see whether 365167484 is divisible by 11, 
                                      start by subtracting:  [3-6+5-1+6-7+4-8+4] = 0; 
                                      therefore 365167484 is divisible by 11.

Rule 10: (Divisibility by 12):If the number is divisible by both 3 and 4, it is also divisible by 12.

Rule 11: (Divisibility by 13) :  Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13,  then so is the original number divisible by 13.

 Example 1:  Determine whether 225 is divisible by 2,3,4,5, 6, 9 and 10.

                     Sol: 
                            225 is not divisible by 2 since the last digit is not 0, 2, 4, 6 or 8.
                            225 is divisible by 3 since the sum of the digits is 9, and 9 is divisible by 3.
                            225 is not divisible by 4 since 25 is not divisible by 4.
                            225 is divisible by 5 since the last digit is 5.
                            225 is not divisible by 6 since it is not divisible by both 2 and 3.
                            225 is divisible by 9 since the sum of the digits is 9, and 9 is divisible by 9.
                            225 is not divisible by 10 since the last digit is not 0.

              Answer is : 225 is divisible by 3,5,9.

Practice Questions :

1.
 Determine whether 35,120 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.

2. The number 477 is divisible by each of the following numbers EXCEPT:  3, 6, 9

3.
 If a number is divisible by 9, then it is also divisible by which number?

4. Which number is divisible by 8?                                                                  
     23,624               
     39,126                                                                            
     120,458                                  

5. Which number is divisible by 6?
     213
     468
     621

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