Test for divisibility of a number by 7 - Vedic Technique

Introduction:
This article will demonstrate how to verify if a numbver is divisible by 7 or not. It will demonstrate using simple vedic ways so that any student, teacher or maths lover can learn it easily.

Testing technique:
1. Double the last digit of the number.
2. Subtract it from the remaining number.
3. Then test the remainder if divisible by 7.
4. If remainder is a large number, repeat steps 1 to 3 again and again till you get a simple number that you can test mentally.

Example:
Let's test 791 to find if it is divisible by 7 or not.
step 1: Lat digit is 1 X 2 = 2
step 2: Remaining number 79 - 2 = 77
step 3: We can say easily that 77 is divisible by 7
Hence, 791 is dividible by 7

Let's test a bit complex number:
7856492

Step 1: 2 X 2 =4
Step 2: 785649 - 4 = 785645 (this is a big number. Repeat step 1 and 2 now)
Step 3: 5 X 2 = 10
Step 4: 78564 - 10 = 78554
Step 5: 4 X 2 = 8
Step 6: 7855 - 8 = 7847
Step 7: 7 X 2 = 14
Step 8: 784 - 14 = 770

Now, easily we can say that 770 is divisible by 7.
Hence the whole complex number 7856492 is divisible by 7.

Hope this helps.

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Test for Divisibility of a number in traditional methods

Introduction:
In traditional methods, we are taught about checking divisibility by numbers like 2, 3, 4, 5, 6, 8, 9, 10 and 11. We will see the divisibility rule for each of the numbers one by one.

Divisibility test by 2:
A number is divisible by 2 if its last digit is divisible by 2.
Means if the last digit of a number is 0, 2, 4, 6, or 8, then it is divisible by 2.

Example: 12, 76, 1546694 are divisible by 2
5, 87, 6865459 are not divisible by 2

Divisibility test by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.

Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 3.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 3.

Divisibility test by 4:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Example: 124 is divisible by 4 as 24(last two digits of 124) is divisible by 4.
12780 is divisible by 4 as 80 is divisible by 4.
962 is not divisible by 4 as 62 is not divisible by 4.

Divisibility test by 5:
A number is divisible by 5 if its last digit is 0 or 5.

Example: 1265 is divisible by 5
230 is divisible by 5
567 is not divisible by 5

Divisibility test by 6:
A number is divisible by 6 if it is divisible by both 2 and 3.

Example: 432 is divisible by 6 as it is divisible by both 2 and 3.
1439 is not divisible by 6.

Divisibility test by 8:
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.

Example: 12108 is divisible by 8
54800 is divisible by 8

Divisibility test by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.

Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 9.
34587: 3 + 4 + 5 + 8 + 7=27 and 27: 2 + 7 = 9. So, 34587 is divisible by 9.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 9.

Divisibility test by 10:
A number is divisible by 10 if its last digit is 0.

Example: 12650 is divisible by 10

Divisibility test by 11:
Find x = sum of odd numbered digits and y = sum of even numbered digits.
If (x-y) is 0 or multiple of 11, then the number is divisible by 11.

Example:
(1) 121: x = 1 + 1 =2
y = 2
x-y = 0
Hence, 121 is divisible by 11.

(2) 879197: x = 8 + 9 + 9 = 26
y = 7 + 1 + 7 =15
x – y = 26 – 15 = 11
Hence, 879197 is divisible by 11.


I will post content for divisibility test by prime numbers like 7, 13, 17, 23 etc which are not taught in our school sylabus.

Regards,
Banshi.

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Vedic Mathematics - Finding Square of a number made easy

Find Square Of a number with Simple and faster Vedic Ways:
Vedic mathematic contains a lot of formulae (Sutra) that not only allows us to do calculations without pen and paper, it also makes our brain to act faster. Now-a-days, to crack in a competitive exam, we must look into two factors, they are SPEED and ACCURACY. By learning Vedic mathematics, one can achieve these two important factors to crack in any competitive exam.

This document contains formulae for finding out square of a number accurately without pen and paper. The formulae are easy to understand and are demonstrated in easy manner with examples.

1. Find Square of a number ending with 5:

1.1 Example: Let’s find out square of 25. a. Break the number to two parts with 2 as first part and 5 as second part
b. Find multiplication of 2 and (2+1), i.e 2 x 3 = 6
c. Find square of 5, i.e. 25
d. Hence, our answer, 25² = 6 25=625
1.2 Lets take another example, i.e. 65 a. 65 = 6 5
b. 6 x (6+1) = 42
c. Square of 5 = 25
d. Hence, 65² = 42 25 = 4225

1.3 Let’s take a 3 digit number, i.e. 125
a. 125 = 12 5
b. 12 x (12 + 1) = 156
c. Square of 5 = 25
d. Hence, 125² = 156 25 = 15625
This way this rule can be used to calculate square of numbers ending with 5 without help of pen and paper.

2. Find Square of a number which is adjacent to a number that ends with 0 or 5:

We can easily find out square of a number that ends with 0 or 5, e.g. 10, 15, 20, 25, 30 etc.
Now we will see how to find out square of an adjacent number like 11, 9, 16, 14, 21, 19 etc
2.1 Example: Let’s find out square of 31.
a. We know square of 30, i.e. 30² = 900
b. Now, 31² = 30² + (30 + 31) = 900 + 61 = 961

2.2 Lets find out square of 46
a. 45² = 2025
b. 46² = 45² + (45 + 46) = 2025 + 91 = 2116

2.3 Lets find out square of 71
a. 70² =4900
b. 71² = 70² + (70 + 71) = 4900 + 141 = 5041
Now, let’s find out numbers which are 1 less to numbers ending with 5 or 0
2.4 Find square of 14
a. 15² = 225
b. 14² = 15² – (14 + 15) =225 – 29 = 196
2.5 Find square of 29
a. 30² = 900
b. 29² = 30² – (29 + 30) = 900 – 59 = 841

3. Find out Square of a number near 100:

Let’s find out square numbers which are close to 100 and are lesser than 100.
3.1 Find square of 97
a. 97 is 3 less than 100 (i.e. -3)
b. 97² = 97 -3 / 03² = 94 / 09 = 9409 (There should be two digits (09 instead of 9) after ‘/’)
3.2 Find square of 96
a. 96 is 4 less than 100 (i.e. -4)
b. 96² = 96 -4 / 04² = 92 / 16 = 9216
3.3 Find square of 87
a. 87 is 13 less than 100 (i.e. -13)
b. 87² = 87 -13 / 13² = 74 / 169 =7569 (There should be two digits(69 out of 169), hence 1 is carry forwarded from 169 and added to 4 of 74)

Let’s find out square of numbers which are close to 100 and are greater than 100.
3.4 Find square of 103
a. 103 is 3 greater than 100 (i.e. +3)
b. 103² = 103 +3 / 03² = 106/09 = 10609
3.5 Find square of 107
a. 107 is 7 greater than 100 (i.e. +7)
b. 107² = 107 +7 / 07² = 114 / 49 = 11449
3.6 Find square of 113
a. 113 is 13 greater than 100 (i.e. +13)
b. 113² = 113 +13 / 13² = 126 / 169 = 12769 (1 is carry forwarded from 169)

I hope this material was helpful to you. I will add some more materials on Addition, Multiplication, Subtraction and Division and other formulae related to Algebra once I compile them.

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