Math Techniques: Learn the Divisibility Rules

Updated on October 23, 2018
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I'm a B.S. Accountancy degree holder with a certificate of Culinary Arts. These two credentials helped me managed our kitchen properly.

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 3

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, it will result to 6 so the whole number is divisble by 3.

Example # 2: 98732614557
The digits result to 57 and 5 plus 7 is 12 so the whole number is divisible by 3.

Divisibility Rule for number 4

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: 200
It is divisible by 4.

Example # 2: 1741643412412
This number is divisible by four because the last two digits, 12, is divisible by four.

Divisibility Rule for number 5

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

Example # 1: 8740245
The number is divisible by 5 because it ends with 5.

Example # 2: 18441440
The number is divisible by 5 because it ends with 0.

Divisibility Rule for number 6

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

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

Example # 1: 8424
The end digit of the number is even while the sum of the digits is 18 which is divisible by 3. Therefore, the number is divisible by 6.

Example # 2: 6756
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

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
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
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 for number 9

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

Example # 1: 2385
The sum of the number is 18. 18 is divisible by 9, so the number is divisible by 9 too.

Example # 2: 5067
Sum of the number is 18. Then again, the number and the sum are both divisible by 9.

Divisibility Rule of number 8

Check if the sum of the last 3 numbers is divisible by 8.

Example # 1: 78672
The last 3 digits is 672. 672 divide by 8 is equal to 84. Therefore, the number is divisible by 8.

Example # 2: 766736
736 divide by 8 is 92. Therefore, the number is divisible by 8.

Divisibility Rule for number 10

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

Example # 1: 4517384010
The given number above ends at 0, which makes the number divisible by 10.

Example # 2: 314141412410
Same thing. This number is divisible by 10 because it ends at 0.

Divisibility Rule for number 11

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
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 differene between the sum of every set is 0, therefore the number is divisible by 11.

Example # 2: 57739
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

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
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
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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