How many times does a leap year occur in a 400-year cycle?
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97
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98
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99
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100
In a 400-year period, there are 97 leap years. This is due to the rules of the Gregorian calendar, which exclude century years not divisible by 400 from being leap years.
Leap Year Rules
A year is a leap year if it is divisible by 4.
However, if the year is divisible by 100, it is not a leap year.
Unless the year is also divisible by 400, then it is a leap year.
Steps to Calculate Leap Years in 400 Years
Total number of years in 400 years: 400
Number of years divisible by 4 (potential leap years):
400/4=100
Number of years divisible by 100 (century years, not leap years unless divisible by 400):
400/100=4
Number of years divisible by 400 (century years that are leap years):
400/400=1
Calculation
Start with the total number of potential leap years (divisible by 4):
100 years
Subtract the century years (divisible by 100, not leap years):
100 - 4 = 96
Add back the years that are divisible by 400 (leap years):
96 + 1 = 97
Conclusion
In a 400-year cycle, there are 97 leap years.
