In this post you will learn how to check divisibility of a number by 8, 9, 10, 11, 12, 15 and 16. After learning divisibility rules of 8, 9, 10, 11, 12, 15 and 16, you will be able to determine quickly, whether a certain number is divisible by a certain number (divisor) or not. For different divisors, the rules are different. Read them one by one and practice them as per exercise given. After a little practice you will be able to memorize all the rules.
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How to check divisibility by 8
Rule: It the last 3 digit of a number is divisible by 8, the number will be divisible by 8. If the last 3 digit of a number is 000 the number will be divisible by 8.
For example the last 3 digits of number number 134800 which are 800 is divisible by 8. Hence, the number 134800 will be divisible by 8. Similarly number 2000, 5000, 9000 shall be divisible by 8 because the last 3 digits of these numbers are 000.
Exercise: Check the divisibility of 123453, 5467854, 123120 by 8.
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How to check divisibility by 9
Rule: If the sum of all digits of a number is divisible by 9, the number will divisible by 9.
For example the number 31293 is divisible by 9 because the sum of all its digits 18 (3+1+2+9+3=15) is divisible by 9.
Exercise: Check the divisibility of 123453, 654435, 5467854, 123120 by 9.
Divisibility rule of 10
Rule: Any number which ends with 0(zero) will be divisible by 10.
For example numbers 340, 23, 450 shall be divisible by 10.
Exercise: Check whether 456, 340, 453 are divisible by 10 or not.
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Divisibility rule of 11
Rule: For any number, if the sum of digits at odd and even places are equal then the number will be divisible by 11. If the difference of sum of digits at odd and even places is divisible by 11 then also the number will be divisible by 11.
Example: Check the divisibility of 1345675 by 11. Sum of digits at odd place is 15 (1+3+6+5) and the sum of digits at even places are 15 (3+5+7). Since both the sum are equal the number 1345675 is divisible by 11.
Example: Check whether 9487456 is divisible by 11 or not. Sum of odd digit=27, Sum of even digit=16, Difference of sum at odd and even = 11. Since the difference 11 is divisible by 11 the number 9487456 will be divisible by 11.
Exercise: Check the divisibility of 12438473, 363523454, 849727291658 by 11.
How to check divisibility by 12
If any number is divisible by 3 and 4 both, the number will also be divisible by 12. Read how to check divisibility by 3 and 4.
For example, the number 144 is divisible is 3 and 4 both. Hence the 144 is divisible 12.
Exercise: Check the divisibility of 4567524 and 4523464 by 12.
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How to check divisibility by 15
Any number which is divisible by 3 and 5 both, the number is also divisible by 15. Read divisibility rule of 3 and 5.
For example, the 255 is divisible by both 3 and 5, hence it is also divisible by 15.
Exercise: Check divisibility of 3468, 345275, 98670 by 15.
Divisibility rule of 16
If last 4 digit of a number is divisible by 16, the number is also divisible by 16.
For example, last 4 digit of 725520 is divisible by 16. Hence, the number is also divisible by 16.
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