Math Shortcuts: Divisibility Rules

Knowing these divisibility rules can make short work of certain math problems.  For example, divisibility rules are helpful when reducing, or simplifying, fractions.  Another type of question that might arise could be like this one:  

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Which is the following is evenly divisible by 9? 

A) 1233

B) 1234

C) 1236

D) 1239

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Here are the basic "tricks" to use when determining divisibility: 

Divisibility by 1:  all whole numbers are, of course, divisible by 1

Divisibility by 2:  the number is even (it ends with 0, 2, 4, 6, or 8) 
 
Divisibility by 3:  the sum of the digits is divisible by 3 
 
Divisibility by 4:  the last two digits is divisible by 4 
 
Divisibility by 5:  the number ends in 0 or 5 
 
Divisibility by 6:  the number is even and the sum of the digits is divisible by 3 

Divisibility by 7:  an example follows:

• 3101
•   310 - take off the last digit of the number, which was 1
•      -2 - double the removed digit and subtract it
•   308
  
•     30 - repeat the process by taking off the 8
•    -16 - double the removed digit and subtract it
•     14 - the result is 14 which is a multiple of 7

 
Divisibility by 8:  the last three digits are divisible by 8 
 
Divisibility by 9:  the sum of the digits is divisible by 9 
 
Divisibility by 10:  the number ends in 0 
 
Divisibility by 11:  add every other digit beginning with the units digit. Subtract the sum of the remaining digits. If the result is 0, the number is divisible by 11.

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Notably missing is a trick for determining divisibility by the number 7.  For that, all "tricks" are complicated and more difficult than just doing the division to check it for yourself.