what is an  osculator?

explain briefly

 Further to the methods as discussed regarding the finding of prime factors,
there is a very useful method to determine divisibility of dividend by a
divisor, especially for numbers ending in 7 & 3. It is called Osculator (in
Verdic Maths) or Check Multiplier (in Speed Maths). Its operation as follows:-

To determine if a number is evenly divisible by another number, first, you need
to know the Osculator number of the divisor, then you multiply the last digit of
the dividend (the unit) by the Osculator number, add the result to the remaining
digits of the dividend. If the final result is divisible by divisor, then the
original dividend is evenly divisible by the divisor.

Let us start with a small number, 19 x 7 = 133, so we know 133 is evenly
divisible by 7, to test it out, the Osculator number of 7 is 5, take the last
digit 3 of dividend 133, multiply it by 5, 3x5=15, add 15 to the remaining
digits of 13, 13+15=28, and 28 is divisible by 7 (7x4=28).
Let us take another bigger number, 37842 with divisor 7, the Osculator number is
5, so 2 x 5 = 10, 10+3784=3794, still can't tell if 3794 is evenly divisible by
7, you repeat the process again, 4 x 5 = 20, 20+379=399, repeat again 9 x 5 =
45, 45+39=84, 84 is divisible by 7 (7x12=84), so 37842 is divisible by 7.
You can also cast out the divisor before adding to the remaining digits, in the
above example, 37842 with divisor of 7 and Osculator of 5, 2 x 5 = 10, cast out
7 will leave 3, add 3 to 3784 equal 3787, repeat the process, 7 x 5 = 35, cast
out 7 or multiple of 7 will leave 0 ending in 378, repeat again 8 x 5 = 40,
casting out 7 leave 5, add to 37 gives 42, 42 is evenly divisible by 7, (6 x7 =
42), so 37842 is divisible by 7.

Hope it helps U.....!!!!