Why isn't 1900 a leap year?

Question

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?

Answer 1

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 $400$.

Answer 2

If you google "leap year" you will find that a year $n$ is a leap year if $n$ is divisible by $4$, except if $n$ is divisible by $100$. If it's divisible by $400$, though, it's still a leap year.

$1900$ is divisible by $100$, but not $400$, so it is not a leap year. $2000$, however, was a leap year.

Answer 3

Leap years under the Julian calendar were those that are divisible by 4.

Leap years under the Gregorian calendar are those that are divisible by 4, except that those divisible by 100 are not, except that those divisible by 400 are.

Answer 4

By definition $n$ is a leap year if (i) $n$ is divisible by $400$ or (ii) $n$ is divisible by $4$ but not divisible by $100$.