**Divisibility rules :**

Here we are going to see the shortcuts to predict one number is divisible by another number with out doing too much calculation.

Once we remember these rules we can easily divide two numbers without calculator.

Learning this topic is more important for all the students who are in school to do visions in a easy way. Divisibility Test

All even numbers are divisible by 2.

The number which ends with one of the following numbers, that is 0, 2, 4, 6 or 8 is known as even numbers.

If the given ends with any of the above numbers, we can say that the given number is divisible by 2.

**Example 1 :**

Check whether 16 is divisible by 2 ?

**Solution :**

Let us test the number 16 is divisible by 2 or not. To test that divide 16 by 2. The result will be 8 (quotient) or the remainder is zero.

Hence, the given number "16" is exactly divisible by 2

To check whether the given number is divisible by 3 or not, we have to add the sum of the digits.

If the sum of the digits is divisible by 3, we can say that it is divisible by 3.

**Example 2 :**

Test whether 252 is divisible by 3?

**Solution :**

To check whether it is divisible by 3 or not we have to calculate the sum of the digits.

252 = 2 + 5 + 2 = 9 ÷ 3 = 3 |

If the last two digits of the given number are zeroes or the last 2 digits are divisible by 4, we can say the given number is divisible by 4.

**Example 3 : **

Test whether 328 is divisible by 4?

**Solution :**

Since the last two digits are not zeroes, we have to check whether the last two digits are divisible 4.

The last two two digits of the given number 328 is 28.Let us check whether it is divisible by 4 or not. |

All the numbers ending in 0 or 5 are divisible by 5

**Example 4 :**

Test whether 105 is divisible by 5 ?

**Solution :**

In the given number 185, the last digit **5**.

Hence, the given number 105 is divisible by 5.

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

Hence all even numbers which are divisible by 3 are divisible by 6

**Example 5 :**

Test whether 5832 is divisible by 6?

**Solution :**

Here the given number is an even number. Hence it is divisible by 2. Now we have to check whether it is divisible by 3 or not for that we have to find the sum of the digits 5 + 8 + 3 + 2 = 18 .

The sum of the digits is divisible by 3. Hence the given number 5832 is divisible by 3.

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

**Example 6 :**

Test whether 998 is divisible by 8 ?

**Solution :**

Here sum of the digits of the given number **9 + 9 + 8 is "26" **which is not divisible by 9 .

Hence, the given number 998 is divisible by 9. |

All numbers which end in 0,that is have 0 in the "ones" place are divisible by 10.

Ex:100,500,450..... are divisible by 10.

**Example 7 :**

Test whether 9470 is divisible by 10 ?

**Solution :**

Here the last digit of the given number is 0.

Hence, the given number 9470 is divisible by 10.

If the difference between the sum of one set of alternate digits and the sum of the other set of alternate digits is 0 or 11 or 22.....the numbers are divisible by 11.

**Example 8 :**

Test whether 198 is divisible by 11?

**Solution :**

In this three digit number the sum of the first and last number = middle number that is **1 + 8 = 9 **So the whole number 198 is divisible by 11.

All the numbers which are divisible by 3 and divisible by 4 are divisible by 12.

**Example 9 :**

Check 8520 is divisible by 12 or not.

**Solution :**

Here the given number is 8520.According to the procedure first we have to check if the given number is divisible by 3.

For that we have to calculate the sum of the digits that is 8 + 5 + 2 + 0 = 15 So it is divisible by 3. | |

To check whether 8520 is divisible by 4 we need to consider the last two digits that is 20 |

So it is divisible by 4.

Hence, the given number 8520 is divisible by 12.

All the numbers which are divisible by 3 and divisible by 5 are divisible by 15.

**Example 10 :**

Check whether the number 41295 is divisible by 15?

**Solution :**

Here we need to check the given number 41295 is divisible by 15 or not.

To check whether the given number is divisible y 15 or not first we have to check whether it is divisible by 3 and it is divisible by 5.

If the given number is divisible by both 3 and 5 we can say the given number is divisible by 15.So, first let us check 41295 is divisible by 3 for that we have to calculate the sum of the digits of the given number.

That is **4 + 1 + 2 + 9 + 5 = 21 **

If we divide the sum of digits 21 by 3 we are getting 0 as the remainder. So we can decide it is divisible by 3.To check whether it is divisible by 5 we need to consider the last digit, that is 5. So it is divisible by 5.

Hence the given number is divisible by 15.

All the numbers which are divisible by 2 and divisible by 9 are divisible by 18.

**Example 11 : **

Check whether 1458 is divisible by 18.

**Solution :**

If the given number is divisible by both 2 and 9.Then we can say it is divisible by 18.

Since the given number ends with 8, it is even number.

All even numbers are divisible by 2.

Now we need to check if it is divisible by 9. To check whether it is divisible by 9 need to calculate the sum of the digits that is,

1 + 4 + 5 + 8 = 18

18 is divisible by 9

Hence, the given number 1458 is divisible by 18.

If the last two digits of a numbers are 00, 25, 50 or 75 is divisible by 25.

**Example 12 :**

Check 3500 is divisible by 25.

**Solution :**

- To check whether the given number is divisible by 25, we have to see the last two digits.
- If the last two digits are either 00 or 25 or 50 or 75 then the given number is divisible by 25.
- The given number is 3500.
- The last two digit is 00.
- So the given number
**3500**is divisible by 25.

After having gone through the stuff given above, we hope that the students would have understood "Divisibility test"

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