VEDIC MATHS-62

  

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 62 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Concept of Positive 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.

Positive Osculators :

The Osculator of a number ending in 9 is considered positive. It is obtained by 

• Dropping 9
• Adding 1 to the remaining number

The Positive Osculator for 19 is 2, for 29 it is 3 and for 59, it is 6.

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

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

Once the Positive 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 Positive Osculators for various numbers.

1. 29

• Dropping 9
• Adding 1 to remaining digit i.e. 2 gives 3.

Answer :

Positive Osculator of 29 is 3.

2. 59

• Dropping 9
• Adding 1 to remaining digit i.e. 5 gives 6.

Answer :

Positive Osculator of 59 is 6.

3. 79

• Dropping 9
• Adding 1 to remaining digit i.e. 7 gives 8.

Answer :

Positive Osculator of 79 is 8.

4. 13

• Here, given number 13 end with 3, we can multiply it by 3, to convert it to a number which ends in 9 i.e. 39.
• Dropping 9
• Adding 1 to remaining digit i.e. 3 gives 4.

Answer :

Positive Osculator of 13 is 4.

5. 7

• Here, given number 7 end with 7, we can multiply it by 7, to convert it to a number which ends in 9 i.e. 49.
• Dropping 9
• Adding 1 to remaining digit i.e. 4 gives 5.

Answer :

Positive Osculator of 7 is 5.

6. 17

• Here, given number 17 end with 7, we can multiply it by 7, to convert it to a number which ends in 9 i.e. 119.
• Dropping 9
• Adding 1 to remaining digit i.e. 1 gives 12.

Answer :

Positive Osculator of 17 is 12.

 7. 23

• Here, given number 23 end with 3, we can multiply it by 7, to convert it to a number which ends in 9 i.e. 69.
• Dropping 9
• Adding 1 to remaining digit i.e. 6 gives 7.

Answer :

Positive Osculator of 23 is 5.

Compute the Positive Osculators for various numbers.

1. 69 Ans Positive Osculator of 69 is 7.
2. 39 Ans Positive Osculator of 39 is 4.
3. 23 Ans Positive Osculator of 23 is 7.
4. 37 Ans Positive Osculator of 37 is 26.
5. 11 Ans Positive Osculator of 11 is 10.

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

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

       

1. 43

2. 69

3. 77

4. 21

5. 89

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

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