Divisibility Properties

Divisibility by 2

When the last digit of a number is either 0 or even (2,4,6,8), then the number is divisible by 2.

Ex - 86, 150, 2358, etc

Divisibility by 3

When the sum of the digits of a number is divisible by 3.

Ex - 2352 : 2+3+5+2=12
       1935 : 1+9+3+5=18

Divisibility by 4

When the last 2-digits of a number is divisible by 4.
Apart from this, the number having two or more zeros at the end. 

Ex - 5728, 3500

Divisibility by 5

Number having 0 or 5 at the end are divisible by 5.

Ex - 1265, 890, 3400, etc

Divisibility by 6

When the number is divisible by both 3 and 2. 

Ex - 258, 1944, etc

Divisibility by 7

A number is divisive 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.

Ex - 658 : 65-2×8 = 65-16 = 49

Divisibility by 8

When the last 3-digits of a number is divisible by 8.
Apart from this, if the last three or more digits are 0.

Ex - 2256, 346000, etc

Divisibility by 9

When the sum of all digits of a number is divisible by 9.

Ex - 5634 : 5+6+3+4 = 18 

Divisibility by 10

When the last digit of a number is 0. 

Ex - 560, 7600, etc

Divisibility by 11

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

Ex - 
2865423
(A)Sum of digits at odd places = 2+6+4+3 = 15
(B)Sum of digits at even places = 8+5+2 =15

Since, A=B
Hence, 2865423 is divisible by 11.

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

Since, A - B = 17 - 6 = 11
Hence, 217382 इस divisible by 11.

Divisibility by 12

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

Ex - 2244 is divisible by both 4 and 3, is also divisible by 12.

Divisibility by 14

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

Ex - 8764 is divisible by both 7 and 2, is also divisible by 14.

Divisibility by 15

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

Ex - 375, 4635, etc

Divisibility by 16

A number is divisible by 16 when the last 4-digit is divisible by 16.

Ex - 126304 : last 4-digits 6304 is divisible by 16.

Divisibility by 18

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

Ex - 936198 is even and divisible by 9, therefore, divisible by 18.

Divisibility by 25

A number is divisible by 25 when its last 2-digits are either 0 or divisible by 25.

Ex - 500, 2425, 3650, etc

Divisibility by 125

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

Ex - 46125, 877250, etc


#rainbowz 

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