Rules for Divisibility

Divisibility by 2: A number is divisible by 2 when the digit at ones place is 0, 2, 4, 6 or 8. еg, 3582, 460, 28, 352.....

Divisibility by 3: A number is divisible by 3 when sum of all digits of a number is a multiple of 3.

eg, 453 4+5+3=12.

12 is divisible by 3 so, 453 is also divisible by 3.

Divisibility by 4: A number is divisible by 4, if the number formed with its last two digits is divisible by 4.

eg, if we take the number 45024, the last two digits form 24. Since, the number 24 is divisible by 4, the number 45024 is also divisible by 4

Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. eg: 10, 25, 60

Divisibility by 6: A number is divisible by 6, if it is divisible both by 2 and 3. eg. 48, 24, 108

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.

eg. 658 65-2×8=65-16=49. As 49 is divisible by 7 the number 658 is also divisible by 7.

Divisibility by 8: A number is divisible by 8, if the number formed by the last 3 digits of the number is divisible by 8.

eg. if we take the number 57832, the last three digits form 832. Since, the number 832 is divisible by 8, the number 57832 is also divisible by 8.

Divisibility by 9: A number is divisible by 9, if the sum of all the digits of a number is a multiple of 9.eg, 684=6+8+4=18.18 is divisible by 9 so, 684 is also divisible 9.

Divisibility by 10: A number is divisible by 10, if its last digit is 0. eg. 20,180, 350,.....

Divisibility by 11: When the difference between the sum of its digits in odd places and in even places is either 0 or a multiple of 11.

eg, 30426

3+4+6=13

0+2=2

13-2=11

As the difference is a multiple of 11 the number 30426 is also divisible by 11.