Leap-year identification (Gregorian rules) — Which of the following listed years is not a leap year?

Introduction / Context:Under Gregorian rules, a year is a leap year if it is divisible by 4, except that century years must be divisible by 400 to be leap years. This question mixes non-century and century values to test the special 400 rule.

Given Data / Assumptions:

• 707 (non-century).
• 800, 1200, 2000 (all century years).
• Apply divisibility by 4 and, for centuries, by 400.

Concept / Approach:First check simple divisibility by 4 for non-century years. For centuries (years ending with 00), being divisible by 4 is not sufficient; they must be divisible by 400 to be leap years.

Step-by-Step Solution:707 ÷ 4 leaves a remainder ⇒ not a leap year.800 ÷ 400 = 2 ⇒ leap year.1200 ÷ 400 = 3 ⇒ leap year.2000 ÷ 400 = 5 ⇒ leap year.

Verification / Alternative check:Centuries 1700, 1800, 1900 are not leap years (not divisible by 400), while 2000 is (divisible by 400). This aligns with the rule we used.

Why Other Options Are Wrong:800, 1200, 2000 all satisfy the 400 rule and thus are leap years; only 707 fails the leap-year criterion.

Common Pitfalls:Assuming any year divisible by 4 is leap, forgetting the century exception.

Final Answer:707