119 Divisibility test of 7

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