What is the formula to find the day of the week if a date is given?

Answer 1

The Day Finding Formula in Brief

(a) Year Digit + (b) 1/4 Value of Year + (c) Date + (d) Month number+ (e) Month Code + (f) Century Code

(g)The total divided by 7, (h) the remainder what comes, will show the day of any date.

The Day Finding Formula Step-wise Detail

Step (a): To take the year digit.

To find the day of any date, at first we shall look up the digits of year which are mostly last two digits.

For an instance: There is 4/4/1975. We shall take last two digits 75 because they are Year digits.

Step (b): (To Find the 1/4 Value of year) OR (Year / 4 Value)

Divide the Year Digit by 4 and its answer should include in the calculation. Note it:- we shall take neither its remainder, nor fractional part but just record the capital value of the answer. For example, in 1998, the year digit is 98 and if we divide it by 4, answer will be 24 and remainder will be 2. We shall just take 24 and leave 2. In the same way, in 2015, the year digit is 15. If we divide 15 by 4, the answer will be 3.75. We shall take just capital value 3 and drop the fractional part .75.

What is the Leap Year?

Leap year means the year which can be divided by 4 such as 1988, 1996, 2000, 2048 etc.

Deduction of (1) in Leap Year

Remember, Leap years whether 1988, 1996, 2000, 2020, 2084 or any others they may be when there happen a date from January 1 to February 29, the number (1) will be subtracted (minus). As in 15/1/2000, 17/2/1992, 25/1/2008, 29/2/1948, years are Leap years and dates are from 1st of January to 29th of February, that's why we shall subtract 1 from the total before dividing by 7.

Note: In addition to Leap year, Every Century that is divided by 4 as 1200's, 1600's etc, we shall deduct (1) from the figure which are from January 1 to February 29. But the Century which can't be divided by 4 as 1st, 14th, 17th, 19th etc, (1) will never be subtracted.

Step (c & d): To Calculate Date & Month Number

After taking the digit of Year and its 1/4 value, we shall include the Date and Month number to find the day of any date. For example April 4, 1975 (OR) 4/4/1975: 4(Date) + 4(Month Number) = 8

Step (e): Month Code

Month codes change from month to month. In accordance with a month, code is applied.

Jan = 0 Feb = 2 March= 1 April = 3 May = 4 June = 6

July = 0 Aug = 2 Sept = 4 Oct = 5 Nov = 0 Dec = 1

Step (f): Century Code

Before applying the Century Code, We need to know the significance of number 4. As we know every fourth year is the year of Leap year. Likewise, the 4th Century is also dealt in a different way. In the same way, 1/4 value is also included. Keeping this, Set of 4 Centuries has been arranged. As the Century Code is given for different Centuries:-

100's = 3 200's = 1 300's = 6 400's = 5

To find out Century Code, divide Century digit by 4. If remainder is 1, Century Code will be 3, if remainder is 2, century code will be 1, if the remainder is 3, the century code will be 6 and if the remainder is 0, then Century Code will be 5. As 1935, Century Digit is 19, if divided by 4, remainder will be 3 and Century Cod will be 6.

In Mathematical way, to find out the century code, first of all divide the Century Digit by 4. In the remainder digit, add 1 and multiply it by 5. Then divide the total by 7, now the remainder will be the century code. For example in 1482, the Century digit is 14. Look at the method below:-

14/4 = Remainder will be 2+1= 3×5 = 15/7= the remainder will be 1, so the Century Cod is (1)

Now the code (1) will be workable from 1400 to 1499.

In another example of 2000, see the formula, 20/4= Remainder 0+1=1×5= 5

As 5 is smaller than 7, it is unnecessary to divide it by 7. For 20th Century, Code will be 5. Along with 2000, 2050, 2093 etc, for the whole 20th Century, the code will be 5.

Step (g):

Taking the total of Year Digit + Year/4 Value + Date + Month Number + Month Code + Century Code, We shall divide the final figure by 7.

Step (h): The Day Table:

After dividing by 7, there comes the remainder which will show a day.

Look at the remainder,

if1, it is Monday, if 2, it is Tuesday, if 3, it will be Wednesday,

if 4, it is Thursday, if 5, it is Friday, if 6, it is Saturday

if it is 0, it is Sunday.

The Day Finding Formula in Brief

As in 22/10/1973

(a) 73(Year) + (b) 18Capital Value (1/4 of 73) + (c) 22(Date) + (d) 10(Month Number) + (e)5(Month Code) + (f) 6(Century Code) = 134

(g) Divide the total 134 by 7, (h) the remainder will be 1. Look up the Day Table. The digit 1 will show Monday. So the day of October 22, 1973 is Monday.

Likewise, find out the day of 18/02/2000:-

(a) 00(Year) + (b) 0 (00Year/4 Value) + (c)18(Date) + (d) 2(Month Number) + (e) 2(Month Code) + (f) 5(Century Code) = 27

(g) As Century Digit 20 can be divided by 4, the date is also within Jan 1 to Feb 29, we will deduct 1 from final figure 27-1=26. Now divide 26 by7= (h) Remainder is 5. Look up Date Table, 5 will show Friday. So 18/02/2000 is Friday.