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.
• If a number 'N' is divisible
by two numbers 'a' and 'b', where a, b are co primes, then 'N' is divisible by
'ab'.
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.
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