Divisibility Rules For Maths A4

Divisibility Rules of Maths
Divisibility Rules for 3: Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.
Divisibility Rule of 4: If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.
Example: Take the number 2308. Consider the last two digits i.e. 08. As 08 is divisible by 4, the original number 2308 is also divisible by 4.
Divisibility Rule of 5: Numbers, which last with digits, 0 or 5 are always divisible by 5.
Divisibility Rule of 6: Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and
the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.
Example: 630, the number is divisible by 2 as the last digit is 0.
The sum of digits is 6+3+0 = 9, which is also divisible by 3. Hence, 630 is divisible by 6.
Divisibility Rules for 7: The rule for divisibility by 7 is a bit complicated which can be understood by the steps given below:
Example: Is 1073 divisible by 7?
From the rule stated remove 3 from the number and double it, which becomes 6.
Remaining number becomes 107, so 107-6 = 101.

Repeat: Last digit of 101, we have 1 x 2 = 2. Remaining number 10 – 2 = 8.
As 8 is not divisible by 7, hence the number 1073 is not divisible by 7.
Divisibility Rule of 8: If the last three digits of a number are divisible by 8,

then the number is completely divisible by 8.
Example: Take number 24344. Consider the last two digits i.e. 344. As 344 is
divisible by 8, the original number 24344 is also divisible by 8.
Divisibility Rule of 9: If the sum of digits of the number is divisible by 9, then

the number itself is divisible by 9.
Divisibility Rules for 11: If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11
completely.
i.e., Sum of digits in odd places – Sum of digits in even places = 0 or a multiple of 11
In order to check whether a number like 2143 is divisible by 11, below is the following procedure.
 Group the alternative digits i.e., digits which are in odd places together and digits in even places together. Here 24 and 13 are two
groups.
 Take the sum of the digits of each group i.e., 2+4=6 and 1+3= 4
 Now find the difference of the sums; 6-4=2, if the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is
the difference which is not divisible by 11.
 Therefore, 2143 is not divisible by 11.
A few more conditions are there to test the divisibility of a number by 11. They are explained here with the help of examples:
If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number.
Example: 3784 Number of digits = 4
Now, 78 + 3 – 4 = 77 = 7 × 11 Thus, 3784 is divisible by 11.
If the number of digits of a number is odd, then subtract the first and the last digits from the rest of the number.
Example: 82907 Number of digits = 5
Now, 290 – 8 – 7 = 275 × 11 Thus, 82907 is divisible by 11.
Form the groups of two digits from the right end digit to the left end of the number and add the resultant groups. If the sum is a
multiple of 11, then the number is divisible by 11.
Ex: 3774 = 37 + 74 = 111 = 1 + 11 = 12, 3774 is not divisible by 11.
Ex: 253 = 2 + 53 = 55 = 5 × 11, 253 is divisible by 11.
Subtract the last digit of the number from the rest of the number. If the resultant value is a multiple of 11, then the original number
will be divisible by 11.
Example: 9647 9647 = 964 – 7 = 957
957 = 95 – 7 = 88 = 8 × 11 Thus, 9647 is divisible by 11
.
Divisibility Rule of 12: If the number is divisible by both 3 and 4, then the number is divisible by 12 exactly.
Example: 5864. Sum of the digits = 5 + 8 + 6 + 4 = 23 (not a multiple of 3)
Last two digits = 64 (divisible by 4)
The given number 5864 is divisible by 4 but not by 3; hence, it is not divisible by 12.
Divisibility Rules for 13: For any given number, to check if it is divisible by 13, we have to add four times of the last digit of the number to
the remaining number and repeat the process until you get a two-digit number. Now check if that two-digit number is divisible by 13 or not.
If it is divisible, then the given number is divisible by 13.
For example: 2795 → 279 + (5 x 4) → 279 + (20) → 299 → 29 + (9 x 4) → 29 + 36 →65
Number 65 is divisible by 13, 13 x 5 = 65.
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Divisibility Rules of Maths

Remaining number becomes 107, so 107-6 = 101.

Divisibility Rule of 8: If the last three digits of a number are divisible by 8,

Divisibility Rule of 9: If the sum of digits of the number is divisible by 9, then

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