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Divisibility Rules. Introduction to Bits and Pieces III. The divisibility rules make math easier! Did you ever wonder how people could tell if something was divisible by a number just by looking at it? These rules are how they do it!

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divisibility rules

Divisibility Rules

Introduction to Bits and Pieces III

divisibility rules1

The divisibility rules make math easier!

  • Did you ever wonder how people could tell if something was divisible by a number just by looking at it?
  • These rules are how they do it!
  • Memorize a few simple rules and simplifying fractions and prime factorization will be so much easier.
Divisibility Rules
divisibility rule for 2

A number is divisible by 2 if

    • It is an even number, or
    • If the last digit of the number is even (0,2,4,6,8)
  • An example is 54,802.
  • What is another example? Come up with your own.
Divisibility Rule for 2
divisibility rule for 3

A number is divisible by 3 ifthe sum (answer to an addition problem) of the digits is divisible by 3.

  • An example is 642.
    • 6 + 4 + 2 = 12 and 12 is divisible by 3, therefore 642 is divisible by 3.
  • What is another example? Come up with your own.
Divisibility Rule for 3
divisibility rule for 4

A number is divisible by 4 if the last two digits of the number are divisible by 4.

  • An example is 948.
    • The last two digits of 948 are 48. 48 is divisible by 4, therefore 948 is divisible by 4.
  • What is another example? Come up with your own.
Divisibility Rule for 4
divisibility rule for 5

A number is divisible by 5 if the number ends in 0 or 5.

  • An example is 999,999,995 because the last digit is 5.
  • What is another example? Come up with your own.
Divisibility Rule for 5
divisibility rule for 6

A number is divisible by 6 if the number is divisible by both 2 and 3 (because 2 x 3 = 6).

  • An example is 72. 72 is even so it is divisible by 2. Also, the sum of the digits of 72 (7 + 2 = 9) is divisible by 3. Therefore, 72 is divisible by 6.
  • What is another example? Come up with your own.
Divisibility Rule for 6
divisibility rule for 8

A number is divisible by 8 ifthe last three digits are divisible by 8 (not as easy a rule).

  • An example is 35,120. 120 is divisible by 8, therefore, 35,120 is divisible by 8.
  • What is another example? Come up with your own.
Divisibility Rule for 8
divisibility rule for 9

A number is divisible by 9 if the sum of the digits is divisible by 9 (almost the same rule as 3).

  • An example is 45. 4+5 = 9, therefore 45 is divisible by 9.
  • Another example is 864. 8+6+4=18, therefore 864 is divisible by 9.
  • What is another example? Come up with your own.
Divisibility Rule for 9
divisibility rule for 10

A number is divisible by 10 if the last digit of the number is 0.

  • An example is 620. 620 ends in zero, therefore, 620 is divisible by 10.
  • What is another example? Come up with your own.
Divisibility Rule for 10
divisibility rule for 12

A number is divisible by 12 if the number is divisible by both 3 and 4 (because 3x4=12).

  • An example is 60. 6+0=6 which means 60 is divisible by 3. Also, 60 is divisible by 4. Therefore, 60 is divisible by 12.
  • What is another example? Come up with your own.
Divisibility Rule for 12
divisibility rule for 15

A number is divisible by 15 if the number is divisible by 3 and 5 (because 3x5=15).

  • An example is 135. 1+3+5= 9 which means 135 is divisible by 3. 135 ends in 5 so it is divisible by 5. Therefore, 135 is divisible by 15.
  • What is another example? Come up with your own.
Divisibility Rule for 15