Test of Divisibility
Divisibility by 2: A number is divisible by 2 if the unit's digit is either zero or divisible by 2.
e.g.: Units digit of 76 is 6 which is divisible by 2 hence 76 is divisible by 2.
Units digit of 330 is 0 so it is divisible by 2.
Divisibility by 3: A number is divisible by 3 if sum of all digits in it is divisible by 3.
e.g.: The number 273 is divisible by 3 since 2 + 7 + 3 = 12 which is divisible by 3.
Divisibility by 4: A number is divisible by 4, if the number formed by the last two digits in it is divisible by 4, or last two digits are zeros.
e.g.: The number 5004 is divisible by 4 since last two digits 04 is divisible by 4.
Divisibility by 5: A number is divisible by 5 if the units digit in the number is either 0 or 5.
e.g.: 375 is divisible by 5 as 5 is in the units place.
Divisibility by 6: A number is divisible by 6 if it is even and sum of all digits is divisible by 3.
e.g.: The number 6492 is divisible by 6 as it is even and sum of its digits 6 + 4 + 9 + 2 = 21 is divisible by 3.
Divisibility by 7:
Step-1: Remove unit's digit. And double it.
Step-2: Subtract it from the rest of the number.
Step-3: Check whether the resulted number is divisible by 7 or not.
Step-4: Repeat the above steps until the resulted number is either 0 (zero) or divisible by 7.
e.g.: Consider the number 10717.
Step-1: Removing the unit's digit i.e. 7. Double of 7 =14.
Step-2: 1071 – 14 = 1057.
Step-3: Now remove 7 from 1057 and double it i.e. 14.
Step-4: 105 – 14 = 91.
Step-5: Now remove 1 and double it i.e. 2.
Step-6: 9 – 2 = 7
The final result 7 is divisible by 7. So the given number i.e. 10717 is also divisible by 7.
Divisibility by 8: A number is divisible by 8, if the number formed by last 3 digits is divisible by 8.
e.g.: The number 6573392 is divisible by 8 as the last 3 digits '392' is divisible by 8.