Divisibility Test
| Divisor | Condition with example |
| 2 | If the unit place of a number is 0 or divisible by 2 i,e even Ex: 2370, 714 and 416 |
| 3 | If the sum of the digits of the given number is divisible by 3. Ex: 567, here 5+6+7 = 18 18 ÷ 3 =6 so 567 divisible by 3 |
| 4 | If last two digits of number is divisible by 4. Ex: 9872, here 72 divisible by 4 hence 9872 also divisible by 4 |
| 5 | If digit at unit place is 5 or 0 Ex: 4870, 9735 |
| 6 | If the number divisible by both 2 and 3 |
| 7 | If twice the number at unit’s place is subtracted from rest of the digits, then the result divisible by 7, entire number divisible by 7 Ex: 875, 87 – 2(5) = 77 here 77 divisible by 7 hence 875 also divisible by 7 |
| 8 | If last three digits are divisible by 8. Ex: 78432 here 432÷8 = 54 hence 78432 divisible by 8 |
| 9 | If the sum of all the digits is divisible by 9. Ex: 8712, 8+7+1+2 = 18 here 18÷9= 2 hence 8712 divisible by 9. |
| 10 | If last digit of number is 0. Ex: 5670 |
| 11 | If the difference between sum of digits at even places and sum of digits at odd places is divisible by 11. Ex: 718135 Sum of digits at odd places 5+1+1 =7 Sum of digits at even places 3+8+7=18 Difference 18-7 =11÷11=1 hence 718135 divisible by 11 |
To find the unit’s place digit of a given exponential
In case of 0,1,5,6 the unit’s place digit is 0,1,5,6 respectively.
In case of 4, 9
- If power is odd @ the unit’s place digit is 4 and 9 respectively.
- If power is even @ the unit’s place digit is 6 and 1 respectively.
In case of 2,3,7,8
See the following example. To find the unit’s place digit of (897)^553
Step-1: 553÷4 gives 1 as remainder, this new remainder taken as new power.
Step-2: (897)^553=(897)^1
Hence unit digit is 7
In case remainder is 0, take new power as 4
Ex: (897)^552 = (897)^0 = (897)^4
7^4= 2401, Hence unit digit is 1.