I.Divisibility by 2:A number is divisible by 2,if its unit digit is 0,2,4,6,8 Ex.1244 is divisible by 2 but 1235 is not divisible by 2.
II.Divisibility by 3:A number is divisible by 3 only when the sum of its digits is divisible by 3. Ex. 234 is divisible by 3 because sum of its digit is divisible by 3.(2+3+4=9,9 is divisible by 3)
III.Divisibility by 4:A number is divisible by 4,if the last two digits of the number are zero or multiple of 4. Ex.49376 is divisible by since 76 is divisible by 4.
IV.Divisibility by 5:A number is divisible by 5 if its unit digit is 5 or 0. Ex.230, 455555,12345.
V.Divisibility by 6:A number is divisible by 6 if it is divisible by both 2 and 3. Ex.974562 is divisible by both 2 and 3 so it is divisible by 6.
VI.Divisibility by 7:The unit digit of the give number is doubled and then it is subtracted from the number obtained after omitting the unit digit.if the remainder is divisible by 7,then the given number is divisible by 7.
Ex.133 is divisible by 7?
Sol:133= 13-3x2=13-6=7,since 7 is divisible by 7 so 133 is divisible by 7.
VII.Divisibility by 8:A numberEx. is divisible by 8 only when the number formed by its last three digits is divisible by 8 or last three digits are 0's.Ex. 45120=120 is divisible by 8,since 45120 is divisible by 8.
VIII.Divisibility by 9:A number is divisible by 9 if the sum of its digit is divisible by 9 Ex.123453 is divisible by 9,since the sum of its digit is divisible by 9(1+2+3+4+5+3=18,18 is divisible by 9).
IX.Divisibility by 10:A number is divisible by 10 only when its unit digit is 0.123420 is divisible by 10 but 125 is not divisible by 10 because 125's unit digit is not 0.
X.Divisibility by 11:A number is divisible by 11 if the difference of the sum of its digits at odd place and the sum of its digits at even place is either 0 or multiple of 11. Ex. 4381729 is divisible by 11
odd place sum (4+8+7+9=28),even place(3+1+2=6)
28-6=22 and 22 is multiple of 11 so 4381729 is divisible by 11.
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