**எண்கள் ( Numbers ) – வகுபடும் தன்மை – அறிமுகம்**

**2 **

A number is divisible by 2, if its unit digit (number in ones place) is any of 0, 2, 4, 6, 8.

Ex. 58694 is divisible by 2 (ones value – 4)

948653 is not divisible by 2 (ones value – 3)

**3 **

When the sum of its digits is divisible by 3

Ex. 695421 is divisible by 3

(6+9+5+4+2+1 = 27 is divible by3)

**4 **

The sum of its last two digits is divisible by 4.

Ex.

* 6879376 is divisible by 4, since last two digit of its number 76 is divisible by 4.

* 496138 is not divisible by 4, since last two digit of its number 38 is not divisible by 4.

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**5**

Its unit digit is 0 or 5.

Ex.

* 76895 is divisible by 5

* 68970 is divisible by 5

**6**

The number is divisible by both 2 and 3.

Ex. 114 is divisible by 6, since

* rule 2 – ones value is 4 , so its divisible by 2

* rule 3 – sum of its digit (1+1+4 = 6) , its divisible by 3.

**8 **

The sum of its last three digits is divisible by 8.

Ex.

* 16789352 is divisible by 8, since last three digit of its number 352 is divisible by 8.

* 576484 is not divisible by 8, since last three digit of its number 484 is not divisible by 8.

**9 **

The sum of its digit is divisible by 9.

Ex.

* 246591 is divisible by 9

(2+4+6+5+9+1 = 27 is divisible by 9)

* 734519 is not divisible by 9.

(7+3+4+5+1+9 = 29 is not divisible by 9)

**10 **

Its unit digit is 0.

Ex.

* 87890 is divisible by 10

* 86945 is not divisible by 10.

**11 **

The difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11.

Ex.

* 29435417

= (sum of odd places) – (sum of even places)

= (7+4+3+9) – (1+5+4+2)

= 23 – 12

= 11

So, 29435417 is divisible by 11.

* 57463822

= (sum of odd places) – (sum of even places)

= (2+8+6+7) – (2+3+4+5)

=23 – 14

=9 , is not divisible by 11.

So, 57463822 is not divisible by 11

**12**

The number must be divisible by 3 and 4

Ex.

* 324 is (3+2+4 = 9) is divisible by 3 and , (24) is divisible by 4 . So 324 is divisible by 12

**15**

The number is divisible by 3 and 5

Ex.

* 390 is (3+9+0 = 12) is divisible by 3 and also is divisible by 5

So 390 is divisible by 15

**25**

Last two digits must be divisible by 25

Ex. 134250

* last two digits of its number 50 is divisible by 25. So, 134250 is divisible by 25

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