Leap-year rule — A (Gregorian) leap year must be divisible by which number (with century exceptions handled separately)?

Difficulty: Easy

Correct Answer: 4

Explanation:


Introduction / Context:
Leap years adjust the calendar to Earth’s orbital period by adding February 29 in certain years. The basic divisibility rule distinguishes common years from leap years, with an extra condition for centuries to avoid overcorrection.


Given Data / Assumptions:

  • Gregorian calendar rules.
  • Basic test for most years.
  • Century exception: years divisible by 100 must also be divisible by 400 to be leap years.


Concept / Approach:
In the Gregorian system: if a year is divisible by 4, it is a leap year, except that century years (ending in 00) are leap only if also divisible by 400 (e.g., 2000 leap, 1900 not). The question asks the base divisor (“must be divisible by”), which is 4, acknowledging that separate century handling exists.


Step-by-Step Solution:

Rule: Divisible by 4 ⇒ leap, unless it is a century year not divisible by 400.Therefore, the fundamental divisor is 4.


Verification / Alternative check:

Examples: 2016 (divisible by 4, not a century) ⇒ leap. 1900 (divisible by 4 and 100 but not by 400) ⇒ not leap. 2000 (divisible by 400) ⇒ leap.


Why Other Options Are Wrong:

5, 6, 9 are unrelated to the Gregorian leap condition; they do not classify leap years correctly.


Common Pitfalls:

Ignoring the century exception (400 rule) and assuming every year divisible by 4 is leap, including 1900 (which is not).


Final Answer:
4

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