divisibilty rules to determine factors of numbers

Here are the divisibility rules to determine if a number is a factor or not.

  • Divisibility by 2:  Any number that is even.  e.g.  72,  80,  1,358
  • Divisibility by 3:  If the sum of the digits is divisible by 3.                                                             e.g. 312 is divisible by 3,  3+1+2=6  6÷3 = 2 
  • Divisibility by 4:  If the last two digits are divisible by 4.  e.g. 5,932   32÷4=8
  • Divisibility by 5:  If the last digit in the number is 5 or 0  e.g. 2,345÷5
  • Divisibility by 6:  A combination of the divisibility rules of 2 & 3.  If the last digit is even and                       the sum of the digits are by 3.                                                                        e.g. 516, 6 is even.  5+1+6=12 12÷3 =4
  • Divisibility by 8:  If the last three digits are divisible by eight.
  • Divisibility by 9:  If the sum of the digits is divisible by nine.  e.g. 459, 4+5+9 = 18,  18÷9=2
  • Divisibility by 10: If the last digit is 0.  e.g. 14,650

 

Divisibility by 7:  This one is a little complicated.   To determine if a number is divisible by 7, take the last digit off the number, double it and subtract the doubled number from the remaining number. If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. This may need to be repeated several times.

 

Example: Is 3101 evenly divisible by 7?

 310   - take off the last digit of the number which was 1
  -2   - double the removed digit and subtract it
 308   - repeat the process by taking off the 8
-16    - and doubling it to get 16 which is subtracted
 14    - the result is 14 which is a multiple of 7