A year is a leap year if it is divisible by 4 (and for century years, divisible by 400). By which of the following numbers must a leap year be divisible?

Introduction / Context:
Under the Gregorian calendar, a leap year typically occurs every 4 years to keep the calendar aligned with the solar year. Century years require an extra check to avoid drift over long periods.

Given Data / Assumptions:

• Standard rule: If a year is divisible by 4, it is a leap year.
• Exception: Century years (like 1800, 1900, 2000) must be divisible by 400 to be leap years.

Concept / Approach:
Among the options, only 4 is the fundamental divisor used in the leap-year test. The extra “400” condition is a refinement for centuries, but 4 remains the base requirement.

Step-by-Step Solution:

Verification / Alternative check:
Examples: 2024 divisible by 4 ⇒ leap; 1900 divisible by 4 but not by 400 ⇒ not leap; 2000 divisible by 400 ⇒ leap.

Why Other Options Are Wrong:
Divisibility by 5/6/9 is unrelated to the leap condition; using them would misclassify many years.

Common Pitfalls:
Forgetting the 400 rule for centuries and mistakenly labeling 1900 as a leap year.

Final Answer:
4.