Dear friends,
When I was in 7th grade in 1972, my teacher taught me the divisibility tests of 2, 3, 4, 5, 6, 8, 9, 10, except 7, then I asked her the divisibility test of 7. On this, she told that there is no test available for 7. I took it as a challenge.
While studying the table of 7 carefully, one day I fount the wonderful method for the divisibility test of 7. Actually, it's very interesting.
This method is published in my book titled "
JADU NAGARI SANKHYANCHI". (Magic world of numbers) written in Marathi by "
Bruhan Mumbai Ganit Adhyapak Mandal, Mumbai" published on 26th Dec 1980.
Procedure:
1) Take a number.
2) Write down its unit placed digit.
3) Double this unit placed digit.
4) Write down our new number excluding unit placed digit.
5) Subtract double of the unit placed digit from our new number.
6) Repeat this till we get a 2 or 1 digit number. If this number is divisible by 7, then our original number is also divisible by 7.
Example-1:
Check
the divisibility of 7 for the number:
|
6902
|
1
|
Your Number
|
A
|
6902
|
6902
|
2
|
Its Unit Placed Digit
|
B
|
2
|
2
|
3
|
Double of Unit placed Digit
|
2B
|
2x2
|
4
|
4
|
Your new Number excluding Unit Placed
Digit
|
C
|
690
|
690
|
5
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
690-4
|
686
|
Repeat the
same procedure
|
6
|
Your Number
|
A
|
686
|
686
|
7
|
Its Unit Placed Digit
|
B
|
6
|
6
|
8
|
Double of Unit placed Digit
|
2B
|
2x6
|
12
|
9
|
Your new Number excluding Unit Placed
Digit
|
C
|
68
|
68
|
10
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
68-12
|
56
|
As 56 is
divisible by 7, our number 6902 is also divisible by 7.
|
Example-2:
Check
the divisibility of 7 for the number:
|
1981
|
1
|
Your Number
|
A
|
1981
|
1981
|
2
|
Its Unit Placed Digit
|
B
|
1
|
1
|
3
|
Double of Unit placed Digit
|
2B
|
2x1
|
2
|
4
|
Your new Number excluding Unit Placed
Digit
|
C
|
198
|
198
|
5
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
198-2
|
196
|
Repeat the
same procedure
|
6
|
Your Number
|
A
|
196
|
196
|
7
|
Its Unit Placed Digit
|
B
|
6
|
6
|
8
|
Double of Unit placed Digit
|
2B
|
2x6
|
12
|
9
|
Your new Number excluding Unit Placed
Digit
|
C
|
19
|
19
|
10
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
19-12
|
7
|
As 7 is
divisible by 7, our number 1981 is also divisible by 7.
|
Example-3:
Check the
divisibility of 7 for the number:
|
20237
|
1
|
Your Number
|
A
|
20237
|
20237
|
2
|
Its Unit Placed Digit
|
B
|
7
|
7
|
3
|
Double of Unit placed Digit
|
2B
|
2x7
|
14
|
4
|
Your new Number excluding Unit Placed
Digit
|
C
|
2023
|
2023
|
5
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
2023-14
|
2009
|
Repeat the
same procedure
|
6
|
Your Number
|
A
|
2009
|
2009
|
7
|
Its Unit Placed Digit
|
B
|
9
|
9
|
8
|
Double of Unit placed Digit
|
2B
|
2x9
|
18
|
9
|
Your new Number excluding Unit Placed
Digit
|
C
|
200
|
200
|
10
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
200-18
|
182
|
Repeat the
same procedure
|
11
|
Your Number
|
A
|
182
|
182
|
12
|
Its Unit Placed Digit
|
B
|
2
|
2
|
13
|
Double of Unit placed Digit
|
2B
|
2x2
|
4
|
14
|
Your new Number excluding Unit Placed
Digit
|
C
|
18
|
18
|
15
|
Subtract double of unit placed digit
from remaining number
|
C-2B
|
18-4
|
14
|
As 14 is
divisible by 7, our number 20237 is also divisible by 7.
|
In the same way, we can check the divisibility test for any number.
ANIL SATPUTE