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.
Divisibility by 9: A number is divisible by 9 if the sum of its digit is divisible by 9.
e.g.: The number 15606 is divisible by 9 as the sum of the digits 1 + 5 + 6 + 0 + 6 = 18 is divisible by 9.
Divisibility by 10: Last digit should be zero.
e.g.: Last digit of 4470 is zero. So, it is divisible by 10.
Divisibility by 11: A number is divisible by 11 if the difference of the sum of the digits at odd places and sum of the digits at the even places is either zero or divisible by 11. (or) Subtract the first digit from a number made by the other digits. If that number is divisible by 11 then the original number is also divisible by 11.
e.g.: In the number 9823, the sum of the digits at odd places is 9+2=11 and the sum of the digits at even places is 8+3=11. Difference between them is 11 – 11 = 0. Hence, the given number is divisible by 11.
e.g.: 14641
1464 − 1 is 1463; 146 − 3 is 143; 14 − 3 = 11, which is divisible by 11, so 14641 is also divisible by 11.
Divisibility by 12: A number is divisible by 12 if it is divisible by 3 and 4.
e.g.: The number 1644 is divisible by 12 as it is divisible by 3 and 4. Here 3 and 4 because they are co-prime to each other.
Divisibility by 13: Repeatedly add 4 times the last digit to the rest until you get a number divisible by 13.
e.g.: 7462 ⇒ 746 + (2×4) = 754 ⇒ 75+ (4×4) = 91
91 is divisible by 13. So, 7462 is also divisible by 13.
Divisibility by 14: The number is divisible by 14 if the given number is divisible by 2 and 7.
e.g: 1232 = 123 – 2 x 2 = 119, 119 is divisible by 7. Hence 1232 is divisible by 14.
Divisibility by 15: The number is divisible by 15 if the given number is divisible by 3 and 5.
e.g: 135 = 1 + 3 + 5 = 9, 9 is divisible by 3. 135 is divisible by 5. Hence 135 is divisible by 15.
Divisibility by 16:
With a 3 digit number: Multiply hundreds digit by 4, then add the last two digits.
e.g.: 352 ⇒ (3×4)+52 = 12 + 52 = 64
64 is divisible by 16. So, 352 is also divisible by 16.
With a more than 3 digit number: The last four digits form a number is divisible by 16.
e.g.: 38512 ⇒ Here is 8512 is divisible by 16. So, 38512 is also divisible by 16.
Divisibility by 17: Subtract 5 times the last digit from the rest.
e.g.: 3961 ⇒ 396 – (1×5) = 391 39 – (1 ⇒ ×5) = 34
34 is divisible by 17. So, 3961 is also divisible by 17.
Divisibility by 18: An even number satisfying the divisibility test by 9 is also divisible by 18.
e.g.: The number 80388 is divisible by 18 as it satisfies the divisibility test of 9.
Divisibility by 19: Add twice the last digit to the rest.
e.g.: 10944 ⇒ 1094 + (4 × 2) = 1102
110 + (2 ⇒ ×2) = 114 11 + (4 ⇒ × 2) = 11 + 8 = 19.
Divisibility by 20: Last digit is zero & tens digit is even.
e.g.: 980; Last digit is zero. And tens digit is even.
Divisibility by 25: A number is divisible by 25 if the number formed by the last two digits is divisible by 25 or the last two digits are zero.
e.g.: The number 7975 is divisible by 25 as the last two digits are divisible by 25.