This is one of the shortcuts to do fast calculations. If you want to know whether a number is divisible by a number in 1-20 read through the following.

1 & 2 - You all know that

3 - (sum of all the digits) should be divisible by 3

eg) 123...1+2+3= 6....6 is divisible by 3...so its divisible by 3

4 - last two (lower most) should be divisible by 4

eg) 3456...56 is divible by 4...hence 3456 is also divisible by 4

5 - number ends with 0 or 5

6 - the number should be divisible by both 2 and 3

7 - oscillator rule (it is at the end)

8 - last 3 digits should be divisble by 8

eg) 4248....248 divisible by 8...hence 4248 also is divisible

9 - (sum of all the digits) should be divisible by 9

10 - number ends with 0

11 - (sum of odd digits - sum of even digits) should be multiple of 11

eg) 121

(1+1)-(2) = 0...multiple of 11...

957

(9+7)-(5) = 11...divisible by 11

12 - should be divisible by both 3 and 4

13 - oscillator rule

14 - should be divisible by both 7 and 2

15 - should be divisible by both 3 and 5

16 - last 4 digits shoulkd be divible by 16

17 - oscillator rule

18 - should be divisible by both 9 and 2

19 - oscillator rule

20 - last 2 digits divisible by 20

Oscillators Rule:

I guess this rule works fine for all prime numbers...2,3,5,7 etc

I will explain it with 2 or 3 examples....

5901 - divisible by 7 or not...?

just multiply 7 by a least number such that the unit place of the result is 9....

that is 7x7= 49 ...leave that 9 and have those remaining digits...ie, 4...add 1 to

it...therefore 4+1=5

now take the last digit alone in the number....ie 1...multiply 5 with it...5

add 5 to the remaining..590+5=595...now last digit is 5...5x5=25 add to the

remaining...59+25=84...divisible by 7...therefore 5901 is divisible by 7

another example

6783 divisible by 17 or not?

17x7 = 119

11+1=12

(for numbers like this...where u have more than 10...or some big numbers...)

then you can do this....

17-12=5

carry the same procedure from here...but u should subtract instead of addition

so 3x5=15

678-15=663

3*5=15

66-15=51...divisible by 17..hence the result...

Related Posts:

How do I learn Maths ?

How many prime numbers are there ?

1 & 2 - You all know that

3 - (sum of all the digits) should be divisible by 3

eg) 123...1+2+3= 6....6 is divisible by 3...so its divisible by 3

4 - last two (lower most) should be divisible by 4

eg) 3456...56 is divible by 4...hence 3456 is also divisible by 4

5 - number ends with 0 or 5

6 - the number should be divisible by both 2 and 3

7 - oscillator rule (it is at the end)

8 - last 3 digits should be divisble by 8

eg) 4248....248 divisible by 8...hence 4248 also is divisible

9 - (sum of all the digits) should be divisible by 9

10 - number ends with 0

11 - (sum of odd digits - sum of even digits) should be multiple of 11

eg) 121

(1+1)-(2) = 0...multiple of 11...

957

(9+7)-(5) = 11...divisible by 11

12 - should be divisible by both 3 and 4

13 - oscillator rule

14 - should be divisible by both 7 and 2

15 - should be divisible by both 3 and 5

16 - last 4 digits shoulkd be divible by 16

17 - oscillator rule

18 - should be divisible by both 9 and 2

19 - oscillator rule

20 - last 2 digits divisible by 20

Oscillators Rule:

I guess this rule works fine for all prime numbers...2,3,5,7 etc

I will explain it with 2 or 3 examples....

5901 - divisible by 7 or not...?

just multiply 7 by a least number such that the unit place of the result is 9....

that is 7x7= 49 ...leave that 9 and have those remaining digits...ie, 4...add 1 to

it...therefore 4+1=5

now take the last digit alone in the number....ie 1...multiply 5 with it...5

add 5 to the remaining..590+5=595...now last digit is 5...5x5=25 add to the

remaining...59+25=84...divisible by 7...therefore 5901 is divisible by 7

another example

6783 divisible by 17 or not?

17x7 = 119

11+1=12

(for numbers like this...where u have more than 10...or some big numbers...)

then you can do this....

17-12=5

carry the same procedure from here...but u should subtract instead of addition

so 3x5=15

678-15=663

3*5=15

66-15=51...divisible by 17..hence the result...

Related Posts:

How do I learn Maths ?

How many prime numbers are there ?

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