Divisibility Rules : Concepts, Divisibility tricks, solved examples.

Divisibility Rules:

Divisibility Rules

Divisibility Meaning : when numerator value can be completely  divided by denominator value, then the numerator value is said to be divisible by the denominator value.

Number System | Ratio & Proportion | Percentage

For example:

20 can be completely divided by 5, hence, the number 20 is divisible by 5.

Tests for divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 15.
Test for divisibility by 2:
If a number has any of the digit's like 0, 2, 4, 6 or 8 in its units place, then that number is divisible by 2.
For example:
12, 26, 88, 94, 104 etc. this number's are completely divisible by 2.
Test for divisibility by 3:
If the sum of all the digit's in a number is divisible by 3, then that number is divisible  by 3.
For example:
15
That is 1 + 5 = 6
6 is divisible by 3. Hence, the number 15 also is divisible by 3.
Test for divisibility by 4:
If the number formed by the digit's in the tens and units places of a number is divisible by 4, then that number also is divisible by 4.
For example:
In the number 3464, the number formed by the digit's in the tens and units places is 64. This number is divisible by 4.
Hence, the number 3464 also is divisible by 4.
Test for divisibility by 5:
If a number has either 0 or 5 in its units place, then that number is divisible by 5.
For example:
In the number 35, the number formed by the digit in the unit place is 5. This number is divisible by 5.
Test for divisibility by 6 :
If a number can be divided by the numbers 2 as well as 3, then that number is divisible by 6.
For example:
The number 24 has 4 in the unit place. Therefore, it is divisible by 2. The sum of the digit's in the 24 is 6. 6 is divisible by 3. Therefore, 24 is divisible by 3. Thus, 24 is divisible by 2 as well as 3. Therefore, it is also divisible by 6.
Test for divisibility by 7 :
If a number is divisible by 7, take the last digit off the number, double it and subtract the doubled number from the remaining number. If the result is zero or evenly divisible by 7, the number is divisible by 7.
For example :
Determine 308 is divisible by 7.
Unit place number = 8×2 =16
Remaining number = 30
Subtracting = 30 - 16 = 14
14 is divisible by 7.
Therefore 308 is divisible by 7.
Test for divisibility by 8 :
If the number formed by the digit's in the hundred, tens and units places of a number is divisible by 8, then that  also is divisible by 8.
For example :
Determine 25488 is divisible by 8.
Hundred, tens and unit place number = 488
488 number is divisible by 8. Therefore 25488 number also divisible by 8.
Test for divisibility by 9 :
If the sum of the digit's in a number is divisible by 9, then that number also is divisible by 9.
For example :
Determine 24975 is divisible by 9.
2 + 4 + 9 + 7 + 5 = 27.
27 is divisible by 9. Therefore 24975 also divisible by 9.
Test for divisibility by 10 :
If a number has 0 in its units place, then that number is divisible by 10.
For example :
Determine 1250 is divisible by 10.
Units place number = 0.
Therefore 1250 is divisible by 10.
Test for divisibility by 11:
If the difference between the sum obtained by adding odd place and even place numbers is zero or divisible by 11 then the number is divisible by 11.
For example :
To determine 275539  is divisible by 11.
Odd places number sum : 9 + 5 + 7 = 21
Even places number sum : 3 + 5 + 2 = 10
Difference = 21 - 11 = 11
Therefore 275539 is divisible by 11.

Related Links :

1. Divisibility Rules :

2. Number System math :

3. Ratio and Proportion :

4. Percentage tricks and shortcuts :

5. Profit and loss math tricks :

6. Average problems tricks and shortcuts :

7. lcm and gcd questions and answers :

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