To know whether a number is divisible by...

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...

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