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Tests of Divisibility

Divisibility by 2: A number is divisible by 2, if its unit's digit is 0 or an even number.
 
Example: 84932 is divisible by 2, while 65935 is not.
 
Divisibility by 3: A number is divisible by 3, if the sum of its digits is divisible by 3.
 
Example-1. 592482 is divisible by 3, since sum of its digits 5 + 9 + 2 + 4 + 8 + 2 = 30 which is divisible by3.
 
Example-2. 864329 is not divisible by 3, since sum of its digits 8 + 6 + 4 + 3 + 2 + 9 = 32 which is not divisible by 3.
 
Divisibility by 4: A number is divisible by 4, if the number formed by last two digits is divisible by 4.
 
Example-1. 892648 is divisible by 4, since the number formed by the last two digits is 48 divisible by 4.
 
Example-2. But 749282 is not divisible by 4, since the number formed by the last two digits is 82 is not divisible by 4.
 
Divisibility by 5: A number divisible by 5, if its unit's digit is either 0 or 5.
 
Example: 20820, 50345, etc.
 
Divisibility by 6: If the number is divisible by both 2 and 3.
 
Example: 35256 is clearly divisible by 2
Sum of digits = 3 + 5 + 2 + 5 + 21, which is divisible by 3
Thus the given number is divisible by 6.
 
Divisibility by 8: A number is divisible by 8 if the last 3 digits of the number are divisible by 8.
 
Example: 2016, 2224 are divisible by 8.
 
Divisibility by 11: If the difference of the sum of the digits in the odd places and the sum of the digits in the even places is zero or divisible by 11.
 
Example. 4832718
(8 + 7 + 3 + 4) - (1 + 2 + 8) = 11 which is divisible by 11.
 
Divisibility by 12: All numbers divisible by 3 and 4 are divisible by 12.
 
Divisibility by 7, 11, 13: The difference of the number of its thousands and the remainder of its division by 1000 is divisible by 7, 11, 13.

How to check whether a given number is prime or not? (for example check 139 is prime or not?)

Step 1: First find Square of Which number is nearest of that number. We find that 139 is nearest of 144 which is square of 12.
 
Step 2: Check is all prime number between 0 and that number. Now we have to check the number between  0-12
 
Step 3: if the given number is not divisible by any of the number that we are checking then the number must be prime number.
 
In above example 139 is not divisible by 2,3,5,7,11 so it is prime number.




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