Write the divisibility rules of number by 2 to11 to introduction
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Divisibility by 2: Any even number or number whose last digit is an even number i.e. 2,4,6,8 including 0 is always completely divisible by 2.
Example: 508 is an even number and divisible by 2 but 509 is not an even number, hence not divisible by 2. Procedure to check whether 508 is divisible by 2 or not is as follow:
Divisibility by 3: Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3 i.e., it is a multiple of 3
Consider a number, 308.To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3 then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.
Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.
Divisibility by 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 a 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 by 5: Numbers with last digit 0 or 5 are always divisible by 5.
Example: 10, 10000, 10000005, 595, 396524850 etc.
Divisibility by 6: Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if 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 by 7: The rule for divisibility by 7 is given below:
Example: Is 1073 divisible by 7?
Divisibility by 8: If the last three digits of a number is divisible by 8, then the number is completely divisible by 8.
Example: Take a 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 by 9: 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
Divisibility by 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.
Divisibility by 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.
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Divisibility rule of 2 = A number is divisible by 2 if its ones digit is 0,2,4,6 or 8
Divisibility rule of 3 = A number is divisible by 3 if the sum of the digits of the number is divisible by 3
Divisibility rule of 4 = A number is divisible by 4 if the number formed by its last two digits is divisible by 4
Divisibility rule of 5 = Any number that ends in either 0 or 5 is divisible by 5
Divisibility rule of 6 = A number is divisible by 6 if its is divisible by 2 and 3 both
Divisibility rule of 7 = A number is divisible by 7 if the difference between twice the once digit and the number formed by the other digits is divisible by 7
Divisibility rule of 8 = A number is divisible by 8 if the number formed by its last three digits is divisible by 8
Divisibility rule of 9 = A number is divisible by 9 if the sum of its digit is divisible by 9
Divisibility rule of 10 = A number is divisible by 10 if its ones digits is 0
Divisibility rule of 11 = A number is divisible by 11 if the difference of the sum of its digits in the odd places and the sum of its digits in the even places is either 0 or divisible by 11