How to Check Leap Years with Century Year Rules?
Leap Year questions test whether a year has 365 or 366 days and often use divisibility rules, century-year exceptions and odd-day calculations. This page explains the leap year formula, identifies leap years with clear examples, and shows the calendar rules used in aptitude problems.
What Is a Leap Year?
A year is a leap year if it is divisible by 4, except for century years. A century year is a leap year only when it is divisible by 400. Therefore, 2024 is a leap year, 1900 is not a leap year, and 2000 is a leap year. A leap year contains 52 complete weeks and 2 extra days because 366 = 52 × 7 + 2.
Leap Year Video Lessons
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Leap Year Rules and Date Matching
Learn how to identify leap years and apply date-matching methods in calendar problems, including determining the corresponding day for given dates.
Leap Year Formula & Tricks
Important Formulas
The year must be divisible by 4, but century years must also be divisible by 400.
Dividing 366 by 7 gives a remainder of 2, so a leap year has 2 odd days.
Dividing 365 by 7 gives a remainder of 1, so an ordinary year has 1 odd day.
Quick Tricks
First check divisibility by 4. If the year is not a century year, it is a leap year. If it ends in 00, ignore the divisibility-by-4 result and check divisibility by 400.
For a year that does not end in 00, divisibility by 4 depends on its last two digits. This makes the test quick.
In every 400-year Gregorian cycle, century exceptions are handled by the divisibility-by-400 rule. Years such as 1600, 2000 and 2400 are leap years, but 1700, 1800, 1900 and 2100 are not.
Leap Year Concepts
Divisibility Rule for Ordinary Years
For ordinary years, inspect the last two digits. If those two digits form a number divisible by 4, the entire year is divisible by 4. For example, 2016 and 2028 are leap years, whereas 2023 and 2025 are not.
Century-Year Exception
A century year ends in 00. Divisibility by 4 alone is not sufficient for such a year. Thus, 1800, 1900 and 2100 are ordinary years, while 1600, 2000 and 2400 are leap years.
Odd Days in a Leap Year
Odd days are the days left after complete weeks are removed. For a sequence of years, add 1 odd day for each ordinary year and 2 odd days for each leap year, then divide the total by 7 to obtain the final remainder.
Counting Leap Years in an Interval
The count of leap years from year 1 through N is floor(N/4) − floor(N/100) + floor(N/400). For an interval from A through B, subtract the count through A − 1 from the count through B.
Leap Year Data Table
Use the structured data below while following the explanation and examples.
Leap Year Classification Examples
Examples showing the divisibility rule for ordinary years and century years.
| Year | Divisible by 4 | Divisible by 400 when needed | Leap year? |
|---|---|---|---|
| 2024 | Yes | Not applicable | Yes |
| 2025 | No | Not applicable | No |
| 1900 | Yes | No | No |
| 2000 | Yes | Yes | Yes |
| 2100 | Yes | No | No |
Note: For years ending in 00, divisibility by 400 decides the result.
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Leap Year Revision Points
Use these rules for quick classification and calendar calculations.
- A leap year has 366 days and February has 29 days.
- A non-century year is a leap year if it is divisible by 4.
- A century year is a leap year only if it is divisible by 400.
- 365 days give 1 odd day; 366 days give 2 odd days.
- The leap-year count through N is floor(N/4) − floor(N/100) + floor(N/400).
- 1900 is not a leap year, but 2000 is a leap year.
Leap Year FAQs
What is the leap year formula?
A year is a leap year if it is divisible by 400, or if it is divisible by 4 but not by 100: (year mod 400 = 0) or (year mod 4 = 0 and year mod 100 ≠ 0).
Is 2024 a leap year?
Yes. 2024 is not a century year and is divisible by 4, so February has 29 days.
Why is 1900 not a leap year?
1900 is divisible by 4 but not by 400. Since it is a century year, it fails the special century-year rule.
Why is 2000 a leap year?
2000 is divisible by 400. Therefore, it satisfies the century-year condition and is a leap year.
How many odd days does a leap year have?
A leap year has 2 odd days because 366 = 52 × 7 + 2.
How many leap years are there from 1 to 2024?
There are 491: floor(2024/4) − floor(2024/100) + floor(2024/400) = 506 − 20 + 5 = 491.