## Wednesday, 24 April 2013

### Chapter 6. Finding The Key Numbers For Centuries (First Two Digits In A Year)

There are basically two ways to find the key numbers for the first two digits in a year. One is a basic way and another one is a quick way. Basic way is lengthy to use as compared to the quick way. Still, we need to know the basic steps before using the quick steps since the quick steps are derived from the basic steps only.

So, let's discuss them one after another.

BASIC STEPS:

STEP 1. Divide the first two digits in a year (19 in case of year 1990) by 4 and find the remainder.

STEP 2. Multiply the remainder by 5.

STEP 3. Divide the above multiplication by 7 and find the remainder. The remainder obtained is the key number for that century.

Example: Let’s find the century key number for year 1990.

While finding the century key number we will consider first two digits only from the year (in this case first two digits are 19). So, now we will follow our basic steps:

STEP 1. Divide 19 by 4 and find the remainder.

Find the multiples of 4 till we get a number which is greater than or equal to 19.
So, we will go one step back i.e. 4 x 4=16. Now, subtract 16 from 19. We get 19-16=3 i.e. our remainder when 19 is divided by 4…

To find remainder using calculator when 19 is divided by 4, we will first divide 19 by 4 and we get 4.75…We will consider digits before decimal point i.e. 4. Now we will multiply 4 by 4 (digit before decimal point) and we get 16 (4 x 4=16). To find remainder when 19 is divided by 4 we subtract our multiplication (16) from 19 we get 3 (19-16=3)… And this is our remainder!

STEP 2. Multiply 3 (remainder) by 5.

3 x 5=15.

STEP 3. Divide 15 (Multiplication) by 7 and find the remainder.

Find the multiples of 7 till we get the number greater than or equal to 15.
7 x 2=14
So, we will go one step back i.e. 7 x 2=14. Now we will subtract 14 from 15 and we get 1 (15-14=1). And this is our remainder.

To find remainder using calculator when 15 is divided by 7, we will first divide
15 by 7 and we get 2.5… We will consider digits before decimal point i.e. 2. Now we will multiply 7 by 2 (digit before decimal point) and we get 14 (7 x 2=14).To find remainder when 15 is divided by 7 we subtract our multiplication (14) from 15 we get 1 (15-14=1)… And this is our remainder.

And remainder thus obtained i.e. 1 is the required key number for century number i.e. 19…

Well, well, well now you must be thinking that there are so many calculations we have to do while finding the key number for century… You are right! But, I am going to share with you few results I have concluded that will make you totally skip the above calculations…!!!

Check them below under QUICK STEPS… :)

QUICK STEPS:

Case 1. Suppose our century number is 16 (as in year 1647). Then after calculations done like in BASIC STEPS we will get century key number for 16 as 0… (You can calculate it if you want.)

Case 2. Suppose our century number is 17 (as in 1785). Then after calculations done like in BASIC STEPS we will get century key number for 17 as 5

Case 3. Suppose our century number is 18 (as in year 1890). Then after calculations done like in BASIC STEPS we will get century key number for 18 as 3

Case 4. Suppose our century number is 19 (as in 1950). We have already calculated century key number for 19 as 1

Case 5. Suppose our century number is 20 (as in year 2002). Then after calculations done like in BASIC STEPS we will get century key number for 20 as 0

Case 6. Suppose our century number is 21 (as in 2140). Then after calculations done like in BASIC STEPS we will get century key number for 21 as 5

Case 7. Suppose our century number is 22 (as in year 2250). Then after calculations done like in BASIC STEPS we will get century key number for 22 as 3

Case 8. Suppose our century number is 23 (as in 2360). Then after calculations done like in BASIC STEPS we will get century key number for 23 as 1

Now what we observe is, the sequence 0, 5, 3, 1 is repeating..So, all we will have to do is, remember this sequence: 0, 5, 3, 1 (respective to century numbers 16, 17, 18, 19…). This sequence will repeat again and again…

That is to it…!!

Now you don’t have to follow BASIC STEPS… You can rely upon QUICK STEPS only, provided you select the key number for century correctly as per the sequence… :)

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