##### DIVISIBILITY RULES

**Divisibility by 2**: The number should have 0, 2, 4, 6, 0 , 2 , 4 , 6 , or 8 as the units digit.

*Example* : 600,812,592,716…….. are divisible by 2

**Divisibility by 3:**The sum of digits of the number must be divisible by 3 .

*Example* : 123(1+2+3=6 which is divisible by 3.So,123 is a multiple of 3),450,813,762……… are divisible by 3

**Divisibility by 4:**The number formed by the tens and units digit of the number must be divisible by 4 .

*Example* :124(hundred’s place and ten’s place number is:24 which is a multiple of 4.So 124 is a multiple of 4),500,672,816,912……. are divisible by 4

**Divisibility by 5:**The number should have 0 or 5 as the units digit.

*Example* :125,675,815,105640,95,415,610,870……. are divisible by 5

**Divisibility by 6:**The number should be divisible by both 2 and 3.

*Example* :126(Its unit place=6.So it is divisible by 2.Sum of digits=1+2+6=9.So it is divisible by 3.Hence,126 is divisible by 6 ),612,900,513…….. are divisible by 6.

**Divisibility by 7:**The absolute difference between twice the units digit and the number formed by the rest of the digits must be divisible by (this process can be repeated for many times until we arrive at a sufficiently small number).

*Example* : 175(Its units place is 5,Twice of 5 is 10.Remaining digits are 17.Now the difference of 17 and 10 is 7 which is divisible by 7.So , 175 is divisible by 7),819,952…. are divisible by 7.

**Divisibility by 8:**The number formed by the hundreds, tens and units digit of the number must be divisible by 8.

*Example:*9400(last 3 digits 400 is divisible by 8.So,9400 is divisible by 8),56080,68960… are divisible by 8.

**Divisibility by 9:**The sum of digits of the number must be divisible by 9.

*Example* : 819(Sum of digits=8+1+9=18,which is a multiple of 9.So,819 is divisible by 9),414, 711,657,549….. are divisible by 9.

**Divisibility by 10:**The number should have 0 as the units digit.

*Example :* 500,610,840,9000,18650……. are divisible by 10.

**Divisibility by 11:**The absolute difference between the sum of alternate pairs of digits must be divisible by 11 .

*Example:*1716(The alternate digits pairs are (1,1) and (7,6).The sum of individual pairs are 1+1=2 and 7+6=13.Their difference is 13-2=11 which is divisible by 11.So,1716 is divisible by 11),121,5918,814….. are divisible by 11.

**Divisibility by 12:**The number should be divisible by both 3 and 4.

*Example* :324(Its sum of digits=3+2+4=9.So it is divisible by 3.Last two digits=24.So,it is divisible by 4.Hence,324 is divisible by 12),804,1392,8112,……. are divisible by 12.

**Divisibility by 13:**The absolute sum between the sum of four times the units digits with the number formed by the rest of the digits must be divisible by 13 (this process can be repeated for many times until we arrive at a sufficiently small number).

*Example*:585(Four times the sum of units digit is 5*4=20.The remaining digits=58.Their sum is 58+20=78 which is a multiple of 13.So,585 is divisible by 13 ),325,637,871,1118 ….. are divisible by 13.

**Divisibility by 25:**The number formed by the tens and units digit of the number must be divisible by 25.

*Example* : 45775(The last two digits = 75 which is a multiple of 25.So,45775 is divisible by 45775),8925,9650,6500 … are divisible by 25