Divisibility Test (Division Rules in Maths)

 

Divisibility Rule of 2 :

If a number is even or a number whose last digit is an even number i.e.  2,4,6,8 including 0, it is always completely divisible by 2.

Example: 234,  384, 64, etc

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Divisibility Rules for 3 : 

if the sum of its digits is divisible by 3.

516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.

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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 6308. Consider the last two digits i.e.  08. As 08 is divisible by 4, the original number 6308 is also divisible by 4.

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Divisibility Rule of 5 :

Numbers, which last with digits, 0 or 5 are always divisible by 5.
Example: 10, 10000, 10000005, 595, 396524850, etc.

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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: 930, the number is divisible by 2 as the last digit is 0.
The sum of digits is 9+3+0 = 12, which is also divisible by 3.
Hence, 930 is divisible by 6.

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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 the number 1408. Consider the last three digits i.e.  408.  is divisible by 8, the original number 6308 is also divisible by 8.

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Divisibility Rule of 9 : The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Example: Consider 78532, as the sum of its digits (7+8+5+3+2) is 25, which is not divisible by 9, hence 78532 is not divisible by 9.

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Divisibility Rule of 10

Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

Example: 10, 20, 30, 1000, 5000, 60000, etc.

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Divisibility Rules for 11

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.

i.e., Sum of digits in odd places – Sum of digits in even places = 0 or a multiple of 11

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