Thursday, July 2, 2015

Divisibility Test Rules along with Examples

Divisibility Tests

Divisibility by different numbers

Rule

Divisibility by 2

When the last digit of a number is either 0 or even, then the number is divisible by 2.

For example : 12, 86, 472, 520 etc

Divisibility by 3

When the sum of the digits of a number is divisible by 3, then the number is divisible by 3. For example:
(i)                  1233   = 1+2+3+3 =9, which is divisible by 3, so 1233 must be divisible by 3.
(ii)                156 = 1+5+6 =12, which is divisible by 3, so 156 must be divisible by 3.

Divisibility by 4

When the number made by last two-digits of a number is divisible by 4, then that particular number is divisible by 4.
Apart from this, the number having two or more zeroes at the end, is also divisible by 4. For example:
(i)                  6428 is divisible by 4 as the number made by its last two digits i.e,. 28 is divisible by 4.
(ii)                The numbers 4300, 153000, 9530000 etc., are divisible by 4 as they have two or more zeroes at the end.

Divisibility by 5

Numbers having 0 or 5 at the end are divisible by 5. For example 45, 4350, 135, 14850 etc.., are divisible by 5 as they have 0 or 5 at the end.

Divisibility by 6

When a number is divisible by both 3 and 2, then that particular number is divisible by 6 also.

For example: 18, 36, 720, 1440 etc., are divisible by 6 as they are divisible by both 3 and 2.

Divisibility by 7

A number is divisible by 7 when the difference between twice the digit at ones place and the number formed by other digits is either zero or a multiple of 7.

For example: 658 is divisible by 7 because 65 -2 x8 = 65 -16 =49. As 49 is divisible by 7, the number 658 is also divisible by 7.

Divisibility by 8

When the number made by last three digits of a number is divisible by 8, then the number is also divisible by 8. Apart from this, if the last three or more digits of a number are zeroes, then the number is divisible by 8. For example

(i)                  2256 = As 256(the last 3 digits of 2256) is divisible by 8, therefore 2256 is also divisible by 8.

Divisibility by 9

When the sum of all the digits of a number is divisible by 9, then the number is also divisible by 9. For example:

(i)                  936819 = 9+3+6+8+1+9 =36 which is divisible by 9. Therefore, 936819 is also divisible by 9.
(ii)                4356 = 4+3+5+6 = 18 which is divisible by 9. Therefore, 4356 is also divisible by 9.

Divisibility by 10

When a number ends with zero, then it is divisible by 10.

For example: 20,30,40, 150, 478970 etc. are divisible by 10.

Divisibility by 11

When the sums of digits at odd and even places are equal or differ by a number divisible by 11, then the number is also divisible by 11.

For example: 2865423  Let us see
Sum of digits at odd places (A) = 2+6+4+3 =15
Sum of digits at even places (B)= 8+5+2=15
A=B
Hence, 2865423 is divisible by 11

(2) 217382  Let us see
Sum of digits at odd places(A)= 2+7+8= 17
Sum of digits at even places(B)= 1+3+2= 6

A – B =17 -6 =11
Clearly, 217382 is divisible by 11.

Divisibility by 12

A number which is divisible by both 4 and 3 is also divisible by 12.

For example: 2244 is divisible by both 4 and 3 .Therefore, it is also divisible by 12.

Divisibility by 14

A number which is divisible by both 7 and 2 is also divisible by 14.

For example: 1232 is divisible by both 7 and 2. Therefore, it is also divisible by 14.

Divisibility by 15

A number which is divisible by both 5 and 3 is divisible by 15 also.

For example: 1275 is divisible by both 5 and 3. Therefore, it is divisible by 15 also.

Divisibility by 16

A number is divisible by 16 when the number made by its last 4-digits is divisible by 16.

For Example: 126304 is divisible by 16 as the number made by its last 4-digits i.e, 6304 is divisible by 16.

Divisibility by 18

A number is divisible by 18 when it is even and divisible by 9.

For example- 936198 is divisible by 18 as it is even and divisible by 9.

Divisibility by 25

A number is divisible by 25 when its last 2-digits are either zero or divisible by 25.

For example: 500, 1275, 13550 are divisible by 25 as last 2-digits of these numbers are either zero or divisible by 25.

Divisibility by 125

A number is divisible by 125 when the number made by its last 3-digits is divisible by 125.

For example: 630125 is divisible by 125 as the number made by its last 3-digits are divisible by 125.



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