VEDIC MATHS-64

 

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 64 from the series of "Vedic maths" blogs. Here in this blog we will learn about "The concept of Negative Osculator"

Concept of Osculator :

The concept of ‘Osculator’ is useful to check the divisibility of a given number by divisors ending with 9 or 1 or a multiple there of.

An osculator is a number defined for any number ending in 9 or 1 and is obtained from the number by a simple mechanism described in this chapter.

The use of Osculators would be severely limited if only these two categories of numbers viz. ending with 9 or 1 were considered. Interestingly, numbers ending with 3 and 7 can also converted to numbers ending with 1 or 9 by a suitable multiplication. The same techniques can be used for all such numbers too.

Osculators are categorized into two main types viz. positive and negative depending on whether the number ends with 9 or with 1.

Reference:

We had already learn about "Concept of Positive Osculator" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-62"

We had already learn about "The Osculation Method for checking divisibility of number by Positive Osculator" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-63"

Negative Osculators :

The Osculator of a number ending in 1 is considered negative. It is obtained by 

• Dropping 1
• Remaining number is Negative Osculator

The Negative Osculator for 11 is 1, for 21 it is 2 and for 51, it is 5.

If the given number does not end in 1 but in 9 or 3 or 7, we can multiply it by 9, 7 or 3 respectively, to convert it to a number which ends in 9 and then compute the Negative Osculator by dropping the 1.

Examples are given below of how to compute the Negative Osculators for various numbers.

Once the Negative Osculator of a number has been computed, it is a simple matter to check the divisibility of any given number by it.

Examples :

Compute the Negative Osculators for various numbers.

1. 21

• Dropping 1
• Remaining digit is Negative Osculator i.e  2.

Answer :

Negative Osculator of 21 is 2.

2. 51

• Dropping 1
• Remaining digit is Negative Osculator i.e  5

Answer :

Negative Osculator of 51 is 5.

3. 81

• Dropping 1
• Remaining digit is Negative Osculator i.e  8

Answer :

Negative Osculator of 81 is 8.

4. 7

• Here, given number 7 end with 7, we can multiply it by 3, to convert it to a number which ends in 1 i.e. 21.
• Dropping 1
• Remaining digit is Negative Osculator i.e  2

Answer :

Negative Osculator of 7 is 2.

5. 9

• Here, given number 9 end with 9, we can multiply it by 9, to convert it to a number which ends in 1 i.e. 81.
• Dropping 1
• Remaining digit is Negative Osculator i.e  8

Answer :

Negative Osculator of 7 is 5.

6. 17

• Here, given number 17 end with 7, we can multiply it by 3, to convert it to a number which ends in 1 i.e. 51.
• Dropping 5
• Remaining digit is Negative Osculator i.e. 5.

Answer :

Negative Osculator of 17 is 5.

 7. 23

• Here, given number 23 end with 3, we can multiply it by 7, to convert it to a number which ends in 1 i.e.161.
• Dropping 1
• Remaining digit is Negative Osculator i.e  16.

Answer :

Negative Osculator of 23 is 16.

Compute the Negative Osculators for various numbers.

1. 69 Ans Osculator of 69 is 62.
2. 39 Ans Osculator of 39 is 35.
3. 23 Ans Osculator of 23 is 16.
4. 37 Ans Osculator of 37 is 11.
5. 11 Ans Osculator of 11 is 01.

The simplicity of this method can be vouched from examples given above.

You may try following example & Compute the Negative Osculators for various numbers.:

       

1. 41

2. 19

3. 27

4. 33

5. 29

In next blog we will discuss about "The Osculation Method for checking divisibility of number by Negative Osculator".     

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I will post my new blog in next week.

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