# Math Techniques: Learn the Divisibility Rules

*I have a B.S. in accounting and a certificate in culinary arts. These two credentials help me efficiently manage our kitchen.*

## Everyday Math

All divisibility rules as discussed above will serve as an effective guideline for kids and even adults to their everyday dealings in life. Without the need of any hi-tech gadgets like ordinary or scientific calculator or even cellphones, everybody can solve a math problem with these basic rules.

Do you know that most people believed that “Math is everywhere”? When we do shopping, checking the clock, paying our meal in the cafeteria or restaurant, driving our car, etc. Meaning math starts as soon as we wake up every morning and ends as soon as we sleep every evening. It makes sense why we really need to love Math no matter how difficult it is to understand sometimes.

## Divisibility Rule for number 2

**Rule:** If the last digit is 0, 2, 4, 6 or 8 (even numbers), the number is divisible by 2.

**Example # 1:** 984

98**4**

The last digit is 4 so the number is divisible by 2.

**Example # 2:** 1007

100**7**

The last digit is 7 so the number is not divisible by 2.

## Divisibility Rule for number 3

**Rule:** Add up the digits. If the sum is divisible by 3, then the number is as well divisible by 3.

**Example # 1: 369**

By adding all the digits,

3 + 6 + 9 = 18

18 / 3 = 6

The sum 18 is divisible by 3 therefore 369 is divisible by 3.

**Example # 2: 98732614557**

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9 + 8 + 7 + 3 + 2 + 6 + 1 + 4 + 5 + 5 + 7 = 57

57 / 3 = 19

The sum 57 is divisible by 3 therefore 98732614557 is divisible by 3.

## Divisibility Rule for number 4

**Rule:** Look at the last two digits of the number. If the number formed by its last two digits is divisible by 4, the number is as well divisible by 4.

**Example # 1: 324**

3**24**

24/4 = 6

It is divisible by 4.

**Example # 2: 1741643412412**

17416434124**12**

12/4 = 3

This number is divisible by four because the last two digits, 12, is divisible by 4.

## Divisibility Rule for number 5

**Rule:** If the last digit is a five or a zero then the number is divisible by 5.

**Example # 1: 874025**

87402**5**

The number is divisible by 5 because it ends with 5.

**Example # 2: 18441440**

1844144**0**

The number is divisible by 5 because it ends with 0.

## Divisibility Rule for number 6

**Rule:** Check 3 and 2. If the number is divisible by both 3 and 2, it is divisible by 6 as well.

If the end digit of the number is even and the sum of the digits is a multiple of 3, then the number is divisible by 6.

**Example # 1: 8424**

**Step # 1: 8424 - 4 is even**

Step # 2: 8+ 4 + 2 + 4 = 18

1 + 8 = 9

The end digit of the number is even while the sum of the digits is 9 which is divisible by 3. Therefore, the number is divisible by 6.

**Example # 2: 6756**

Step # 1: 675**6** - 6 is even

Step # 2: 6 + 7 + 5 + 6 = 24

2 + 4 = 6

The end digit of the number is even and the sum of the digits is 24 which make it divisible by 3 so to 6.

## Divisibility Rule for number 7

**Rule:** To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number.

**Example # 1: 406**

Step # 1: 6 * 2 = 12

Step # 2: 40 - 12 = 28

28 / 7 = 4

Double the last digit to get 12 and subtract that from 40 to get 28. 28 is divisible by 7, therefore the number is divisible by 7 as well.

**Example # 2: 378**

Step # 1: 8 * 2 = 16

Step # 2: 37 - 16 = 21

21 / 7 = 3

8 multiply by 2 equals 16. 16 subtracted from 37 is 21. 21 is divisible by 7, that makes the number is divisible by 7 too.

## Divisibility Rule of number 8

**Rule:** Check if the last 3 numbers is divisible by 8.

**Example # 1:** 78672

78**672**

672 / 8 = 84

The last 3 digits is 672. 672 divide by 8 is equal to 84. Therefore, the number is divisible by 8.

**Example # 2:** 766736

766**736**

736 divide by 8 is 92. Therefore, the number is divisible by 8.

## Divisibility Rule for number 9

**Rule:** Add the digits. If that sum is divisible by nine,then the original number is as well.

**Example # 1: 2385**

2 + 3 + 8 + 5 = 18

18 / 9 = 2

The sum of the number is 18. 18 is divisible by 9, so the number is divisible by 9 too.

**Example # 2: 6399**

6 + 3 + 9 + 9 = 27

27 / 9 = 3

Sum of the number is 27. Then again, the number and the sum are both divisible by 9.

## Divisibility Rule for number 10

**Rule:** If the number ends in 0, it is divisible by 10

**Example # 1: 4517384010**

451738401**0**

The given number above ends at 0, which makes the number divisible by 10.

**Example # 2: 314141412410**

31414141241**0**

Same thing. This number is divisible by 10 because it ends at 0.

## Divisibility Rule for number 11

**Rule:** Add the first, third, fifth, seventh and so on digit of the number. Then, add the second, fourth, sixth, eighth and so on digit of the number. If the difference, including 0, is divisible by 11, then so is the number.

**Example # 1: 14904857**

Step # 1: **1**4**9**0**4**8**5**7

1 + 9 + 4 + 5 = 19

Step # 2:1**4**9**0**4**8**5**7**

4 + 0 + 8 + 7 = 19

19 - 19 = 0 =

Sum of 1, 9, 4 and 5 is equal to 19. While the sum of 4, 0, 8 and 7 is equal to 19. The difference between the sum of every set is 0, therefore the number is divisible by 11.

**Example # 2: 57739**

Step # 1: **5**7**7**3**9**

5 + 7 + 9 = 21

Step # 2: 5** 7**7

**3**9

7 + 3 = 10

21 - 10 = 11

Sum of 5, 7 and 9 is 21. Then the sum of 7 and 3 is 10. The difference between 21 and 10 is equal to 11 and is divisible by 11. Therefore the number is divisible by

11.

## Divisibility Rule for number 12

**Rule:** Check for divisibility rule of numbers 3 and 4. The given number must be both divisible by 3 and 4 to make the it divisible by 12.

**Example # 1: 312**

Step # 1: 3 + 1 + 2 = 6

6 / 3 = 2

Step # 2: 3**12**

12 / 4 = 3

Divisibility rule for number 3: The sum of all digits of the number is equal to 6, therefore, the number is divisible by 3.

Divisibility rule for number 4: The last two digit of the number is 12, therefore, the number is divisible by 4.

The number passed the divisibility rule of both 3 and 4, that makes the number divisible by 12.

**Example # 2: 8244**

Step # 1: 8 + 2 + 4 + 4 = 18

18 / 3 = 6

Step # 2: 82**44**

44 / 4 = 11

Divisibility rule for number 3: The sum of all digits is equal to 18, that makes the number divisible by 12.

Divisibility rule for number 4: The last two digit of the number is 44 which is divisible by 4.

The number therefore is divisible by 12 because it passed the divisibility rule of numbers 3 and 4.

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