Divisibility Rules

The Divisibility Rules

The DivisibilityRules

These rules let you test if one number isdivisible by another, without having to do too much calculation!


Divisible by:


If:


Examples:


2


The last digit is even (0,2,4,6,8)


128 is

129 is not


3


The sum of the digits is divisible by 3


381 (3+8+1=12, and 12÷3 = 4) Yes

217 (2+1+7=10, and 10÷3 = 3 1/3No


4


The last 2 digits are divisible by 4


1312 is (12÷4=3).7019 is not


5


The last digit is 0 or 5


175 is

809 is not


6


The number is divisible by both 2 and 3


114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

 

308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3No


7


If you double the last digit and subtract it from the rest of the number and the answer is:

  0, or

  divisible by 7

(Note: you can apply this rule to that answer again if you want)


672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7No


8


The last three digits are divisible by 8


109816 (816÷8=102) Yes

216302 (302÷8=37 3/4No


9


The sum of the digits is divisible by 9

 

(Note: you can apply this rule to that answer again if you want)


1629 (1+6+2+9=18, and again, 1+8=9) Yes

2013 (2+0+1+3=6) No


10


The number ends in 0


220 is.221 is not


11


If you sum every second digit and then subtract all other digits and the answer is:

  0, or

  divisible by 11


1364 ((3+4) - (1+6) = 0Yes

3729 ((7+9) - (3+2) = 11Yes

25176 ((5+7) - (2+1+6) = 3No


12


The number is divisible by both 3 and 4


648 .(By 3? 6+4+8=18 and 18÷3=6 Yes. .By 4? 48÷4=12 Yes) Yes

524 .(By 3? 5+2+4=11, 11÷3= 3 2/3 No. .Don't need to check by 4.)No


 



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