How does the largest-remainder method distribute seats among political parties?

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Map of Canada displaying the results of the 2008 federal election by province and territory, with regions shaded to indicate the leading party's share of the popular vote: blue for Conservative, red for Liberal, light blue for Bloc Quebecois, and orange for New Democratic Party. Each area is labeled with the number of seats won by each party, and a legend at the bottom summarizes national seat totals for each party. — election Canada's 2008 federal election results.

The largest-remainder method (also known as the greatest-remainder formula) distributes legislative seats through a two-step process based on a calculated electoral quota.1

The Allocation Process

Establishing the Quota: First, an electoral quota is determined, typically by dividing the total number of votes cast in a district by the number of available seats.1
Initial Allocation: Each party’s total vote count is divided by this quota. A party is immediately awarded one seat for every full quota it has achieved.1
Distributing Remainders: If seats remain after the initial allocation, they are distributed sequentially to the parties that possess the largest "remainders"—the leftover votes each party has after its full quotas have been subtracted.1

This process continues until all available seats in the district have been filled. Compared to largest-average formulas, the largest-remainder method generally provides better representation for smaller political parties.1