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.
In the same way, we can check the divisibility test for any number.
ANIL SATPUTE
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.
Example1:
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

C2B

6904

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

C2B

6812

56

As 56 is
divisible by 7, our number 6902 is also divisible by 7.

Example2:
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

C2B

1982

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

C2B

1912

7

As 7 is
divisible by 7, our number 1981 is also divisible by 7.

Example3:
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

C2B

202314

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

C2B

20018

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

C2B

184

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