Chapter 7. Finding The Key Number For The Last Two Digits In The Year

This is one of the most important steps. To explain this step, I will again take my example only i.e. year 1990… Now, last two digits in year 1990 form a number 90. To calculate key number for 90 (last two digits in year), follow the steps mentioned below:

STEP 1. Divide the number formed (90 in this case) by 4 and find the quotient.

(Note: Till now we were finding the reminder for division but this is the only step where we have to find quotient.)

Method to find the quotient is easy and similar to the method to find the remainder. First find the multiples of 4 till we get a number which is greater than or equal to 90.

4 x 23=92 (See multiplication table for 4) So, we will go one step back i.e. 4 x 22=88. And this 22 is nothing but our quotient…!

Note: If 90 were exact multiple of 4 then no need to go one step back. E.g. If our number would have been 92 instead of 90 then we would have got 4 x 23=92 i.e. 92 is exact multiple of 4. Therefore our quotient would have been 23.

To find quotient using calculator is even easier. Just divide 90 by 4, we get 22.5… And the number before decimal point is our quotient i.e. 22.

STEP 2. Subtract 1 from 90 (i.e. last two digits from year).

(Note: We always need to subtract 1 only.)

90-1=89.

STEP 3. Add quotient (from STEP 1) and subtraction result (from STEP 2).

22+89=111.

STEP 4. Divide the addition from STEP 3 (in this case 111) by 7 and find the remainder.

Find the multiples of 7 till we get the number greater than or equal to 111.

7 x 16=112 (See multiplication table for 7)

So, we will go one step back i.e. 7 x 15=105. Now we will subtract 105 from 111 and we get 6 (111-105=6). And this is our remainder!

To find remainder using calculator when 111 is divided by 7, we will first divide 111 by 7 and we get 15.8571…We will consider digits before decimal point i.e. 15. Now we will multiply 7 by 15 (digit before decimal point) and we get 105 (7 x 15=105). To find remainder when 111 is divided by 7 we subtract our multiplication (105) from 111 we get 6 (111-105=6)… And this is our remainder!

And this remainder (i.e. 6) is nothing but our key number for last two digits in year (i.e. 90 in this case).

So, this is the method to find the key number for the last two digits in the year. It needs a little practice and you can master this. :)

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