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).

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