Leap Year Calculation: 1890 to 1909

To find the number of leap years between $1890$ and $1909$, we need to apply the rules for leap years to the years in this range.

A year is a leap year if it meets the following criteria:

• It is divisible by $4$.
• However, if a year is divisible by $100$, it is NOT a leap year, unless...
• The year is also divisible by $400$.

The range of years to consider is from $1891$ to $1908$ (exclusive of $1890$ and $1909$ as per the common interpretation of 'between').

Identifying Potential Leap Years

First, list the years within the range ($1891$ to $1908$) that are divisible by $4$:

• $1892 \div 4 = 473$
• $1896 \div 4 = 474$
• $1900 \div 4 = 475$
• $1904 \div 4 = 476$
• $1908 \div 4 = 477$

The potential leap years are $1892, 1896, 1900, 1904, 1908$.

Applying the Century Rule

Now, check these potential years against the century rule:

• The year $1900$ is divisible by $100$.
• To be a leap year, $1900$ must also be divisible by $400$.
• Since $1900 \div 400 = 4.75$ (not an integer), the year $1900$ is NOT a leap year.
• The other potential leap years ($1892, 1896, 1904, 1908$) are not divisible by $100$, so they remain leap years based on divisibility by $4$.

Final Count of Leap Years

The leap years between $1890$ and $1909$ are:

• $1892$
• $1896$
• $1904$
• $1908$

There are a total of $4$ leap years in this period.