From the following years, which one is not a leap year according to the Gregorian calendar: 1996, 1984, 1863 or 2004?

Introduction / Context:
Leap year identification questions check whether you know the basic divisibility rules that determine when February has 29 days instead of 28. Here, you are given a list of four years and must pick the one that is not a leap year. Correct application of the rules is crucial, especially to distinguish years that are clearly divisible by 4 from those that are not.

Given Data / Assumptions:

• Years to examine: 1996, 1984, 1863, 2004 and an extra distractor, 1884.
• We use the Gregorian calendar rules for leap years.
• None of these years are century years (none end in 00), so the century rule is not directly involved.

Concept / Approach:
The leap year rule for non-century years is simple:

• If a year is divisible by 4, then it is a leap year.
• If a year is not divisible by 4, it is a common (non-leap) year.

Because none of the given years are century years, we only need to check divisibility by 4 to decide whether each is a leap year or not.

Step-by-Step Solution:
Step 1: Check 1996. Since 1996 / 4 = 499 exactly, 1996 is divisible by 4 and is therefore a leap year. Step 2: Check 1984. 1984 / 4 = 496 exactly, so 1984 is also divisible by 4 and is a leap year. Step 3: Check 2004. 2004 / 4 = 501 exactly, so 2004 is divisible by 4 and is a leap year. Step 4: Check 1863. 1863 / 4 = 465.75, not an integer. Therefore, 1863 is not divisible by 4 and is not a leap year. Step 5: Check 1884 (as an additional example). 1884 / 4 = 471 exactly, so it is a leap year and not the required answer.

Verification / Alternative check:
Another quick check for divisibility by 4 is to look at the last two digits of the year. If the number formed by the last two digits is divisible by 4, then the whole year is divisible by 4. For example, 96, 84 and 04 are all divisible by 4, but 63 is not. This confirms that 1996, 1984 and 2004 are leap years, while 1863 is not.

Why Other Options Are Wrong:
1996, 1984 and 2004 are all divisible by 4 and hence incorporate a 29th February, making them leap years. Any additional year such as 1884 is also divisible by 4. Choosing any of these would contradict the leap year rule for non-century years. Only 1863 fails the divisibility test.

Common Pitfalls:
Some candidates mistakenly think that any year ending with an even digit is a leap year, or they miscalculate the division by 4. Remember that not every year divisible by 4 is a leap year if it is a century year, but for non-century years, divisibility by 4 is sufficient. Here, the century rule does not apply, simplifying the problem.

Final Answer:
The year that is not a leap year among the given options is 1863.