Rules of Divisibility

Meaning of Divisibility

When one number divided by other number and result come a whole number, it means first number is divisible by second number.

Examples:

If first number is 8 and second number 4, 8÷4=2, here the result is 2 that is a whole number so 8 is divisible by 2.

• Divisibility by 2 : If unit place of any number is either even number or 0, the number will be divisible by 2. Example : 4, 8, 10, 5468 etc.

• Divisibility by 3: if the sum of digits of any number is divisible by 3, the number will be divisible by 3. Example :  345 is divisible by 3 because 3+4+5= 12. Here 12 is divisible by 3 therefore 345 will also be divisible by 3.

• Divisibility by 4 : If last two digit number of any number is divisible by 4, the number will be divisible by 4.

• Divisibility by 5 : If the last digit of the number is either 0 or 5, the number will be divisible by 5. Example: 10, 50, 653785 etc. are divisible by 5.

• Divisibility by 6 : A number will be divisible by 6, if the number is divisible by 2 and 3.   Example: 12, 18, 24 etc are divisible by 6 because all these numbers are by 2 and 3.

• Divisibility by 8 :  If last three digits of any number is divisible by 8 or last three digits are "000", the number will be divisible by 8. Example: 856000, 456008, 1201024 are divisible by 8 because in first number last three digits are "000", in second number last three digits are "008" which is divisible by 8 and in third number last three digits are "024" which are also divisible by 8, therefore all these three numbers are divisible by 8.

• Divisibility by 9 : If sum of digits of any number is divisible by 9, the number will be divisible by 9. Example : 4563, 981, 7857 etc are divisible by 9 because sum of digits of first number(4+5+6+3=18) 18 is divisible by 9, thus these numbers are divisible by 9.

• Divisibility by 10 : If unit place of any number is "0" Zero, the number will be divisible by 10. Example : 20, 50, 100, 50000, 55550, etc are divisible by 10.

• Divisibility by 11 : If, of any number, difference between sum of odd place digits and sum of even place digits is either "0" or divisible by 11, the number will be divisible by 11. Example : 54285 is divisible by 11 because in this number sum of odd place digits (5+2+5=12) and sum of even place digits (8+4=12) now difference (12-12=0), therefore this number will be divisible by 11

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