what is the divisibility rules of 4,6,7,8,9,11and12
Answers
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 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:
Divisibility rule for 7
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.
Repeating the process one more times, we have 1×2=2
Remaining number 10 – 2 = 8.
As 8 is not divisible by 7, hence the number 1073 is not divisible by 7.
Divisibility by 8: If the last three digits of a number are 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 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.
In order to check whether a number like 2143 is divisible by 11 following is the 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.
Divisibility Rule for 12
A number is divisible by 12 if it is divisible by both 3 and 4. The reason this is true is because 12 = 3 × 4. Knowing this, the only part that you may not understand is when a number is evenly divisible by 4. This is the case when the last two digits of the number are divisible by four.
If you have trouble looking at a two digit number and figuring out if it is divisible by four, try the following:
If the right-most digit is odd, it is not divisible by four.
If the right-most digit is 0, 4, or 8, the next digit to the left must be even.
If the right-most digit is 2, or 6, the next digit to the left must be odd.
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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 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 8: If the last three digits of a number are 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.