Math Techniques: Learn the Divisibility Rules

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Everyday Math

All divisibility rules as discussed above will serve as an effective guideline for kids and even adults in their everyday dealings in life. Without the need for any high-tech gadgets like an 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 go shopping, check the clock, pay for our meal in the cafeteria or restaurant, drive our car, etc. This means 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

984

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

Example # 2: 1007

1007

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

3 + 6 + 9 = 18

18 / 3 = 6

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

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Example # 2: 98732614557

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

324

24/4 = 6

It is divisible by 4.

Example # 2: 1741643412412

1741643412412

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

874025

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

Example # 2: 18441440

18441440

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: 6756 - 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 are divisible by 8.

Example # 1: 78672

78672

672 / 8 = 84

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

Example # 2: 766736

766736

736 divided 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

4517384010

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

Example # 2: 314141412410

314141412410

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 to the digit of the number. Then, add the second, fourth, sixth, eighth, and so on to the digit of the number. If the difference, including 0, is divisible by 11, then so is the number.

Example # 1: 14904857

Step # 1: 14904857

1 + 9 + 4 + 5 = 19

Step # 2: 14904857

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: 57739

5 + 7 + 9 = 21

Step # 2: 57739

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

Example # 1: 312

Step # 1: 3 + 1 + 2 = 6

6 / 3 = 2

Step # 2: 312

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 digits of the number is 12, therefore, the number is divisible by 4.

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

Example # 2: 8244
Step # 1: 8 + 2 + 4 + 4 = 18

18 / 3 = 6

Step # 2: 8244

44 / 4 = 11

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

Divisibility rule for number 4: The last two digits 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.