Why isn't 1900 a leap year? I searched leap years online and found that 1900 is not, contrary to what _I_ thought, a leap year. But, why is it not if 1900 is divisible by 4: $\frac{1900}{4} = 475$ My brother was working on his math (and he obviously got it wrong and asked me for help, so.. here I am), and the question was: Which year, after $1899$ is a leap year? Well, after finding that $1900$ is indeed divisible by 4, his intuition led him to believe that $1900$ was thus the next leap year. However, the answer is $1904$. Would someone mind explaining this?

The length of a Tropical Year is approximately $365.2422$ mean solar days.

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**Julian Calendar**

The Julian Calendar approximates the length of a tropical year as $$ 365.25=365+\tfrac14 $$ Therefore, it adds one leap year every $4$ years.

Thus, every year that is divisible by $4$ is a leap year.

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**Gregorian Calendar**

The Gregorian Calendar approximates the length of a tropical year as $$ 365.2425=365+\tfrac14-\tfrac1{100}+\tfrac1{400} $$ Therefore, it adds one leap year every $4$ years, skipping one every $100$ years, but adding one back every $400$ years.

Thus, every year that is divisible by $4$ is a leap year except for those divisible by $100$ but not $400$.