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What are the 10 Divisibility rules?

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nini2000 | Student, Undergraduate | eNotes Newbie

Posted November 11, 2011 at 3:15 AM via web

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What are the 10 Divisibility rules?

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted November 11, 2011 at 6:45 AM (Answer #1)

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2:  number ends in 0, 2, 4, 6, or 8

3:  add the digits, the sum will equal a number divisible by 3

4:  the last two digits will be divisible by 4

5:  number ends in 0 or 5

6:  number is divisible by 2 and 3

7:  double the last digit, subtract that from the rest of the number, the difference will be divisible by 7 or will equal 0

8:  the last 3 digits are divisible by 8

9:  add the digits, the sum will equal a number divisible by 9

10:  number ends in 0

 

The divisibility rule for 7 is the most difficult, so here is an example:

672

double the last digit (2) = 4

subtract from the rest of the number:  67-4 = 63

63 is divisible by 7, therefore 672 is divisible by 7

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matthew0109 | Student | Honors

Posted November 12, 2011 at 12:21 PM (Answer #2)

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All even numbers are divisible by 2.  (All numbers ending in 0, 2, 4, 6,8,)

To find out if a number is divisible by 3, you add all the digits together in the number, and then find the sum.  Once you have found the sum of all the digits, divide that number by 3 and if get a whole number, then the number is divisible by 3.

To find out if a number is divisible by 4, the last 2 digits must be divisible by 4.  If you divide it by 4 and get a whole number, then the entire number is divisible by. For example:358912 The last two digits are 12.  12/4=3 Therefore, the entire number is divisible by 4.

Numbers that end in 5 or a 0, are automatically divisible by 5.

If the number is divisible by 2 and 3, it is also divisible by 6.

To find out if a number is divisible by 7, you need to take the last digit in a number, double it, and subtract the last digit in the number from the rest of all of the other digits.

35008 is divisbile by 8 because when you add the last three digits together 0+0+8=8 8/8=1.  Therefore, 35008 is divisibile by 8.

To find out if a number is divisible by 9, add all of the digits up and then you can divide that number by 9, and if the number comes out to be a whole number, then it is divisible by 9.

If a number ends in a 0, it is divisible by 10.

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