Leap-year identification — Which of the following is a leap year under the Gregorian rules?

Introduction / Context:Non-century years are leap years if divisible by 4. Century years require divisibility by 400.

Given Data / Assumptions:

• Options: 1146, 1254, 2100, 1128.
• 2100 is a century year; must be divisible by 400 to be leap.

Concept / Approach:Check divisibility by 4 (and 400 for century years).

Step-by-Step Solution:1146 ÷ 2 = 573 (odd), so not divisible by 4 → not leap.1254 ÷ 2 = 627 (odd), so not divisible by 4 → not leap.2100: century not divisible by 400 → not leap.1128: divisible by 4 (1128 ÷ 4 = 282) → leap year.

Verification / Alternative check:Further, 1128 ÷ 8 = 141 with remainder 0, also indicating February 29 exists that year under Gregorian convention.

Why Other Options Are Wrong:They violate the divisibility rules (either not by 4, or century not by 400).

Common Pitfalls:Treating all numbers divisible by 2 as leap years; ignoring the century rule.

Final Answer:1128 is a leap year.