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What are the Rules of Divisibility?

Updated on September 5, 2012
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The Rules of Divisibility

There are quick little rules or tricks that help people know when a larger number is divisible by a basic fact number.

Any number less than 12 can be considered a basic fact number, but not all of them have divisibility rules.

Divisible by 2?

Any even number is divisible by 2. So that means any numbers that ends in 0, 2, 4, 6, or 8.


Divisible by 3?

Add the digits of the number together, if the sume of those digits is a product of 3 than it is divisible by 3.

Example

45 : 4 + 5 = 9 : 9 is divisible by 3 therefore 45 is divisible by 3

Source

Divisible by 4?

If the last two digit of the number are divisible by 4 then the number is divisible by 4.

Why? Simply because 4 goes into 100 therefore anything beyond a hundred is a multiple of 100.

Divisible by 5?

Any number that ends in 0 or 5 is divisible by 5.

Example:

2130 ends in 0 and is therefore divisible by 5. 5551 ends in 1 and is NOT divisible by 5.

Source

Divisible by 6?

If a number is divisible by 2 and 3 it is automatically divisible by 6.


Why? Well let's think about what we know about 2, 3, and 6. 2 & 3 are the prime factors of 6 therefore creating the perfect 6 divisibility rule.

No Rule for 7

BOOHOO HOO there is no easy fact rule for 7 so just do the division. There is some long obtuse algorithm that just isn't worth the time or energy to learn.

Divisible by 8?

There are two parts to the rule for 8

If the digit in the hundreds place is even than refer to the last two digits of the number, if that number is divisible by 8 then that entire number is divisible by 8.

If the digit in the hundreds place is odd than add 4 to the last two digits. If the last two digit plus 4 is divisible by 8 than the entire number is divisible by 8.


424 : 24 divided by 8 is divisible therefore 424 is divisible by 8

544 : 5 is odd : 44 + 4 is 48 48 is divisible by 8 therefore 544 is divisible by 8

Divisible by 9?

Add all of the digits of the number together. If the sum of the digits is divisible by 9 then the number is divisible by 9.


Divisible by 10?

All numbers that end is zero are divisible by 10

Why do I need to know this?

Knowing the rules of divisibility will help you become more confident in your math understanding and conceptual knowledge of numbers. It will help you at some point in life that I can guarantee you. It will help you become faster and more proficient in your math abilities and a stronger student.

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