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Divisibility Rules

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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!
- Memorize a few simple rules and simplifying fractions and prime factorization will be so much easier.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.