**Divisibility Rules, Meaning, Definition, in Math - Mathematics:**

**This lesson presents divisibility rules for the numbers 2,3,4,5,6,7,8,9, and 10**

**Divisibility rules of whole numbers are very useful because they help us to quickly determine if a number can be divided by 2,3,4,5,9, and 10 without doing long division.**

Divisibility means that you are able to divide a number evenly

For instance, 8 can be divided evenly by 4 because 8/4 = 2. However, 8 cannot be divided evenly by 3.

To illustrate the concept, let's say you have a cake and your cake has 8 slices, you can share that cake between you and 3 more people evenly. Each person will get 2 slices.

However,if you are trying to share those 8 slices between you and 2 more people, there is no way you can do this evenly. One person will end up with less cake

In general, a whole number x divides another whole number y if and only if you can find a whole number n such that

x times n = y

For instance, 12 can be divided by 3 because 3 times 4 = 12

When the numbers are large, use the following divisibility rules:

**Rule #1: divisibility by 2**

A number is divisible by 2 if it's last digit is 0,2,4,6,or 8.

For instance, 8596742 is divisible by 2 because the las t digit is 2.

**Rule # 2: divisibility by 3:**

A number is divisible by 3 if the sum of its digits is divisible by 3

For instance, 3141 is divisible by 3 because 3+1+4+1 = 9 and 9 is divisible by 3.

**Rule # 3: divisibility by 4**

A number is divisible by 4 if the number represented by its last two digits is divisible by 4.

For instance, 8920 is divisible by 4 because 20 is divisible by 4.

**Rule #4: divisibility by 5**

A number is divisible by 5 if its last digit is 0 ot 5.

For instance, 9564655 is divisible by 5 because the last digit is 5.

**Rule # 5: divisibility by 6**

A number is divisible by 6 if it is divisible by 2 and 3. Be careful! it is not one or the other. The number must be divisible by both 2 and 3 before you can conclude that it is divisible by 6.

**Rule # 6: divisibility by 7**

To ckeck divisibility rules for 7, study carefully the following two examples:

Is 348 divisible by 7?

Remove the last digit, which is 8. The number becomes 34. Then, Double 8 to get 16 and subtract 16 from 34.

34 − 16 = 18 and 18 is not divisible by 7. Therefore, 348 is not divisible by 7

Is 37961 divisible by 7?

Remove the last digit, which is 1. The number becomes 3796. Then, Double 1 to get 2 and subtract 2 from 3796.

3796 − 2 = 3794, so still too big? Thus repeat the process.

Remove the last digit, which is 4. The number becomes 379. Then, Double 4 to get 8 and subtract 8 from 379.

379 − 8 = 371, so still too big? Thus repeat the process.

Remove the last digit, which is 1. The number becomes 37. Then, Double 1 to get 2 and subtract 2 from 37.

37 − 2 = 35 and 35 is divisible by 7. Therefore, 37961 is divisible by 7.

**Rule #7:divisibility by 8**

A number is divisible by 8 if the number represented by its last three digits is divisible by 8.

For instance, 587320 is divisible by 8 because 320 is divisible by 8.

**Rule #8: divisibility by 9**

A number is divisible by 9 if the sum of its digits is divisible by 9.

For instance, 3141 is divisible by 9 because the sum of its digits is divisible by 9.

**Rule # 9: divisibility by 10**

A number is divisible by 10 if its last digits is 0

For instance, 522480 is divisible by 10 because the last digit is 0.

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