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**Divisibility Test For Different Numbers**

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Divisibility Test by 2 The last digit is even (0,2,4,6,8) are divisible by 2 For Example:- 20, 42, 124, 1606, 2288

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**Divisibility Test by 3 The sum of the digits is divisible by 3.**

For Example:- ⇒ 63 (6+3=9) and 9 is divisible by 3. Hence 63 is also divisible by 3. ⇒ 381 (3+8+1=12) and 12 is divisible by 3. Hence 381 is also divisible by 3.

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**Divisibility Test by 4 The last 2 digits are divisible by 4**

For Example:- ⇒ and 24 is divisible by 4 ⇒ 4720 and 20 is divisible by 4

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**Divisibility Test by 5 The last digit is 0 or 5 For Example :-**

50, 1225, 2110, 38265

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**Divisibility Test by 6 The number is divisible by both 2 and 3**

For Example :- ⇒ 36 (it is divisible is 2 and 3) ⇒ 108 (it is divisible is 2 and 3)

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**Divisibility Test by 7 For Example :- ⇒ 154 = 15 - 4 x 2 = 7**

Multiply last digit by 2 & subtract it from rest of the number . If the answer is 0 or multiple of 7, then the number is divisible by 7. For Example :- ⇒ 154 = x 2 = 7 ⇒ 672 = 67 – 2 x 2 = 63

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**Divisibility Test by 8 The last three digits are divisible by 8**

For Example :- ⇒ 1128 : Last 3 digits is divisible is 8, hence the number is also divisible by 8. ⇒ :

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**Divisibility Test by 9 The sum of the digits is divisible by 9**

For Example :- ⇒ 1629: ( = 18) which is divisible by 9, hence the number is also divisible by 9. ⇒ : ( = 9) which is divisible by 9,

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**Divisibility Test by 10 The number ends in 0. For Example :-**

40, 120, 360, 5890

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**Divisibility Test by 11 For Example :-**

If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11 For Example :- ⇒1364 ((3+4) - (1+6) = 0). Hence it is divisible by 11 ⇒ 3729: ((7+9) - (3+2) = 11). Hence it is Divisible by 11.

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Divisibility Test by 12 12= 3 x 4 The number is divisible by both 3 and 4. For Example :- ⇒ 648 : By 3? 6+4+8=18 is divisible by 3 By 4? 48÷4=12 is divisible by 4. Since it is divisible by both 3 & 4. Hence it is also divisible by 12.

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Divisibility Test by 13 Multiply 4 to the last digit and add with the remaining digits. If the result is divisible by 13, then it is also divisible by 13.Apply this rule over and over again as necessary. For Example :- ⇒ 169: x 4 = = 52. Since 52 is divisible by 13. Hence the given number is also divisible by 13. ⇒ : x 4 = 5070 5070 = X 4 = 507 507 = x 4 = 78. Since 78 is divisible by 13. Hence the given number is also divisible by 13.

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**Divisibility Test by 14 14 = 7 X 2**

Check if the last digit of the original number is odd or even. If the number is odd, then the number is not divisible by fourteen. If the number is even, then apply the divisibility rule For 7. For Example :- ⇒ 1232: By 2? Last digit is even number. Hence 1232 is divisible by 2. By 7? 1232 = x 2 = 119 ; 119 is divisible by 7. Hence 1232 is also divisible by 14.

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**Divisibility Test by 15 Number should be divisible by 3 as well as 5.**

15 = 3 x 5 Number should be divisible by 3 as well as 5. Apply divisibility rule of 3 and 5. For Example :- 11445 : By 3? = 15 which is divisible by 3. By 5? last digit of the number is 5. Hence it is divisible by 5. Therefore, is also divisible by 15

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Divisibility Test by 16 Divide the last 4 digits by 16 and if it is divisible by 16 then any given number is divisible by 16. For Example :- ⇒ : Since Last 4 Digits are divisible by 16. Therefore, is also divisible by 16. ⇒ : Since Last 4 Digits are divisible by 16. Therefore, is also divisible by 16.

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**Divisibility Test by 17 For Example :- ⇒ 765:**

Multiply the last digit by 5. Subtract it from the rest. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary. For Example :- ⇒ 765: 76-5x5 = 51. Since 51 is divisible by 17. Hence 765 is also divisible by 17 ⇒ 3978: 397-5x8=357 357=35-5x7=0. So 3978 is divisible by 17.

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**Divisibility Test by 18 Apply divisibility rule of number 2 and 9.**

18=2×9 Apply divisibility rule of number 2 and 9. For Example :- ⇒ 9342: By 2? Last digit is 2. Hence it is divisible by 2. By 9? =18, which is divisible by 9. Since 9342 is divisible by 2 & 9 . Therefore 9342 is also divisible by 18

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Divisibility Test by 19 Multiply the last digit by 2 and add it to the remaining digits. Repeat this process until you arrive at a smaller number whose divisibility you know. For Example :- ⇒ 12483, 3x2 = 6 and = , 4x2 = 8 and = , 3x2 = 6 and 13+6 = 19 Since 19 is divisible by 19, therefore is also divisible by 19.

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**Divisibility Test by 20 The last digit should be 0 .**

The second last digit should be even. For Example :- 3240, 45560, ,

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